Communication method and device based on folding hypercube network

Abstract

The embodiment of the invention provides a communication method and device based on a folding hypercube network, and the method comprises the steps: obtaining two edge-disjoint spanning trees and an unused path in a four-dimensional folding hypercube network, and carrying out the communication of the four-dimensional folding hypercube network based on the two edge-disjoint spanning trees and the unused path in the four-dimensional folding hypercube network, through the first construction method and the second construction method, the target number of edge-disjoint spanning trees in the n-dimensional folding hypercube network are determined, communication between nodes in the network is completed through the target number of edge-disjoint spanning trees, construction of all edge-disjoint spanning trees in the n-dimensional folding hypercube network is achieved, and the network performance is improved. According to the method, network nodes can communicate through multiple paths, the fault-tolerant capability of communication in the folding hypercube network and the security of information transmission are improved, and meanwhile, the method can be applied to a distributed algorithm for resisting man-in-the-middle attack so as to confirm and locate the occurrence of the man-in-the-middle attack.

Description

Technical Field

[0001] The present invention relates to the network field of cloud computing, and in particular to a communication method and device based on a folded hypercube network. Background Art

[0002] As a well-known and common topological network, the hypercube network has a wide range of applications in computer science, sociology, medicine, network security, etc. Research on the connectivity, Hamiltonian properties, and independent spanning tree construction schemes of the hypercube network and its variants can further explore the advantages of the network and improve its utilization.

[0003] As an optimized topology of the hypercube, the folded hypercube network has many advantages over the hypercube network, such as lower message congestion, lower communication delay, and higher communication performance. On this basis, further research on the folded hypercube network can improve the fault tolerance and security of communication in the folded hypercube network, as well as the distributed algorithm for resisting man-in-the-middle attacks. Summary of the invention

[0004] In view of the above problems, a communication method and device based on a folded hypercube network is proposed to overcome the above problems or at least partially solve the above problems, including:

[0005] A communication method based on a folded hypercube network is applied to an n-dimensional folded hypercube network, wherein the n-dimensional folded hypercube network includes 2 n network nodes, acyclic paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree, paths between two adjacent network nodes form edge paths, and multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network form unused paths, the method comprising:

[0006] Get two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network;

[0007] In the case where n is greater than 4, based on the two edge-disjoint spanning trees and the unused paths in the 4-dimensional folded hypercube network, a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network are determined by a first construction method and a second construction method; wherein the first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and the unused paths in the m-dimensional folded hypercube network, and the second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and the unused paths in the m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n;

[0008] By constructing a non-intersecting tree with the target number of edges, the above 2 n Communication between any two of the network nodes.

[0009] Optionally, in the n-dimensional folded hypercube network 2 n Each network node is represented by a binary string of length n.

[0010] Optionally, the value of the target number is a value obtained by rounding up n / 2, and the value of the number of network nodes in the unused path is a value obtained by rounding up (n+1) / 2.

[0011] Optionally, when n is an odd number, determining a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network includes:

[0012] Based on the two edge-disjoint spanning trees and the unused paths in the 4-dimensional folded hypercube network, recursively executing the second construction method to determine n-1 / 2 edge-disjoint spanning trees and the unused paths in the n-1-dimensional folded hypercube network;

[0013] Based on the n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1 dimensional folded hypercube network, a first construction method is executed to determine (n+1) / 2 edge-disjoint spanning trees in the n dimensional folded hypercube network.

[0014] Optionally, when n is an even number, determining a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network includes:

[0015] Based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, the second construction method is recursively executed to determine n / 2 edge-disjoint spanning trees and unused paths in the n-dimensional folded hypercube network.

[0016] Optionally, executing the first construction method includes:

[0017] Obtaining isomorphic first and second m-dimensional folded hypercube networks, as well as m / 2 edge-disjoint spanning trees and first and second unused paths in the first and second m-dimensional folded hypercube networks, and respectively increasing a highest bit of the binary strings corresponding to the network nodes in the first and second m-dimensional folded hypercube networks to 0 and 1, respectively;

[0018] Connecting the isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the first and second m-dimensional folded hypercube networks respectively through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the first and second unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network;

[0019] The network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network are connected to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the m-th edge of each network node in the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network, and the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network are connected to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the first m edge paths in the second unused path, so as to obtain the m / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network; wherein the m-th edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth bit;

[0020] The binary string corresponding to each network node in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network is complemented to obtain the corresponding network node in the first m-dimensional folded hypercube network, and connected to the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network.

[0021] Optionally, executing the second construction method includes:

[0022] Obtaining isomorphic third, fourth, fifth, and sixth m-dimensional folded hypercube networks, as well as m / 2 edge-disjoint spanning trees and third, fourth, fifth, and sixth unused paths in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks, and respectively increasing the two highest bits of the binary strings corresponding to the network nodes in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks to 00, 10, 11, and 01, respectively;

[0023] The first m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the third and fourth m-dimensional folded hypercube networks are respectively connected through the edge paths formed by connecting the first m / 2-2 network nodes in the same position in the third and fourth unused paths, the first m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks are respectively connected through the edge paths formed by connecting the first m / 2-2 network nodes in the same position in the fourth and fifth unused paths, and the first m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks are respectively connected through the edge paths formed by connecting the first m / 2-1 network nodes in the same position in the fifth and sixth unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network;

[0024] Connecting the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fourth and fifth unused paths, connecting the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fifth and sixth unused paths, connecting all network nodes in the third m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-dimensional edges of all network nodes in the third m-dimensional folded hypercube network, and obtaining the m / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network; wherein the m-dimensional edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth position;

[0025] Connecting the network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through all edge paths in the fourth unused path;

[0026] Connecting the network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through all edge paths in the fourth unused path;

[0027] Connecting the network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through all edge paths in the sixth unused path, to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network;

[0028] Based on (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network, unused paths in the m+2-dimensional folded hypercube network are obtained.

[0029] A communication device based on a folded hypercube network is applied to an n-dimensional folded hypercube network, wherein the n-dimensional folded hypercube network includes 2 n network nodes, acyclic paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree, paths between two adjacent network nodes form edge paths, multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network form unused paths, n is an integer greater than or equal to 4, and the device comprises:

[0030] A four-dimensional spanning tree acquisition module, used to obtain two edge-disjoint spanning trees and unused paths in a four-dimensional folded hypercube network;

[0031] An n-dimensional spanning tree construction module is used to determine a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network through a first construction method and a second construction method when n is greater than 4; wherein the first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in the m-dimensional folded hypercube network, and the second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in the m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n;

[0032] A path module is used to generate a tree without intersection through the target number of edges to complete the 2 n Communication between any two of the network nodes.

[0033] An electronic device comprises a processor, a memory and a computer program stored in the memory and capable of running on the processor, wherein the computer program implements the communication method based on a folded hypercube network as described above when executed by the processor.

[0034] A readable storage medium stores a computer program, and when the computer program is executed by a processor, the communication method based on a folded hypercube network as described above is implemented.

[0035] The embodiments of the present invention have the following advantages:

[0036] In an embodiment of the present invention, by obtaining two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network, when n is greater than 4, based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network is determined through a first construction method and a second construction method. The first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in an m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network. The second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in an m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n. The 2 is completed through the target number of edge-disjoint spanning trees. n The invention realizes the communication between any two of the network nodes, realizes the construction of all edge-disjoint spanning trees in the n-dimensional folded hypercube network, enables the network nodes to communicate through multiple paths, improves the fault tolerance of communication in the folded hypercube network, and the security of information transmission, and can also be applied to the distributed algorithm for resisting man-in-the-middle attacks to confirm and locate the occurrence of man-in-the-middle attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solution of the present invention, the accompanying drawings required for use in the description of the present invention will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0038] Figure 1 is a topological structure of a three-dimensional hypercube network provided by some embodiments of the present invention;

[0039] Figure 2 is a topological structure of a three-dimensional folded hypercube network provided by some embodiments of the present invention;

[0040] Figure 3 is a flowchart of the steps of a communication method based on a folded hypercube network provided by some embodiments of the present invention;

[0041] Figure 4 It is a schematic diagram of steps for constructing an edge-disjoint spanning tree of an odd-dimensional folded hypercube provided by some embodiments of the present invention;

[0042] Figure 5 It is a structural block diagram of a communication method and device based on a folded hypercube network provided by some embodiments of the present invention. DETAILED DESCRIPTION

[0043] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] As an optimized topology of hypercube, the folded hypercube network has many advantages: (1) In the broadcast field, the communication between any two vertices (i.e., network nodes) in an n-dimensional hypercube network requires at most n hops, while the communication between any two vertices in an n-dimensional folded hypercube network requires at most only (n / 2 rounded up) jumps, so its communication / broadcast time can be saved by 50%; (2) In terms of communication delay, the average distance between two vertices in the n-dimensional folded hypercube network is significantly smaller than that in the n-dimensional hypercube network, and the message density is also smaller than that in the n-dimensional hypercube network, so in the n-dimensional folded hypercube network FQ n When communicating in the network, the message congestion is lower, the communication delay is lower, and the communication performance is higher.

[0045] In recent years, the problem of finding edge-disjoint spanning trees (EDSTs) in interconnected networks has become particularly common. In addition to its theoretical significance, the solution to this problem can be applied in many practical fields. If there are multiple edge-disjoint spanning trees in an n-dimensional folded hypercube network, then the paths in this edge-disjoint spanning tree can be used for: (1) fault-tolerant broadcast: n edge-disjoint paths between two vertices can still communicate normally in the presence of n-1 faulty edges, and the same is true for broadcast; (2) secure information distribution: n edge-disjoint paths between two vertices are each responsible for 1 / n copies of the information, so only the starting point and the end point can obtain the complete information, ensuring the security of the information; (3) distributed algorithms to resist man-in-the-middle attacks, etc.

[0046] Studies have shown that n-dimensional folded hypercube network FQ n At most constructible The edge-disjoint spanning tree.

[0047] For the folded hypercube network, when 2≥ the dimension of the folded hypercube network≥1, there is one edge-disjoint spanning tree in the folded hypercube network, and when 4≥ the folded hypercube network≥3, there are two edge-disjoint spanning trees in the folded hypercube network. The construction structures in these two cases are relatively easy and can be constructed manually. However, for the case where the dimension of the folded hypercube network is ≥5, its structure is very complicated, and it is difficult to directly obtain the corresponding number of edge-disjoint spanning trees through manual construction.

[0048] In one embodiment of the present invention, for the case where the dimension of the folded hypercube network is ≥5, a 4-dimensional folded hypercube network may be constructed for communication between network nodes in an n-dimensional folded hypercube network.

[0049] The present application embodiment provides a communication method based on a folded hypercube network, which is applied to an n-dimensional folded hypercube network. The n-dimensional folded hypercube network includes 2 n network nodes, acyclic paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree, paths between two adjacent network nodes form edge paths, and multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network form unused paths.

[0050] like Figure 3 As shown, the communication method based on the folded hypercube network may specifically include the following steps:

[0051] Step 301, obtaining two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network.

[0052] Based on the above description, firstly, two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network can be obtained by manual construction.

[0053] In some embodiments of the present invention, the n-dimensional folded hypercube network has 2 n Each network node is represented by a binary string of length n.

[0054] In order to facilitate the description and understanding of the solution of the present invention, any vertex x of the n-dimensional folded hypercube network (i.e., any network node in the n-dimensional folded hypercube network) can be represented by a binary string of length n (i.e., any node in the n-dimensional folded hypercube network including 2 n network nodes), that is: x n-1 x n-2 ...x0; complement of vertex x That is, each bit of the binary string representing the vertex is inverted, that is:

[0055] Vertex x (1) To network node x (n) The path between them is P, (x (1) , x (2) ) is represented by vertex x (1) With vertex x (2) An edge path between two adjacent network nodes (i.e., an edge path is formed by the path between different edge paths. In a path, it is necessary to ensure that any two vertices are different from each other, so there are no two identical edges in a path. A path of length n can be expressed as: (1) -x (2) -…-x (n+1) .

[0056] It should also be noted that for the n-dimensional folded hypercube network FQ n , n-dimensional hypercube network Q n Each vertex in can be a binary string of length n, where each two connected vertices differ by only one bit, such as Figure 1 As shown, the topological structure of the three-dimensional hypercube network Q3 is presented. n is an n-dimensional hypercube network Q n A variant structure of , based on its topological structure, further connects every two complementary vertices to form, such as Figure 2 As shown, the topological structure of the three-dimensional folded hypercube network FQ3 is presented.

[0057] For n-dimensional folded hypercube network FQ n Subgraph of Given a binary string a of length less than n, FQ n All connected vertices with prefix a in can form FQ n The sub-network of Represents the topology of the subnetwork.

[0058] Edge-disjoint means that if P1 and P2 are two paths in a network, if edge (x, y) is an edge path in P1, then path P2 does not contain edges (x, y) and (y, x), that is, there is no identical edge path in the two paths, then P1 and P2 are said to be edge-disjoint.

[0059] The loop-free paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree. An edge-disjoint spanning tree means that if T1 and T2 are two spanning trees in a folded hypercube network, if the edge (x, y) is an edge in T1, then tree T2 does not contain the edges (x, y) and (y, x), that is, there are no identical edges in the two trees, then T1 and T2 are called two edge-disjoint spanning trees in the network.

[0060] The unused paths are formed by multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network.

[0061] Specifically, two edge-disjoint spanning trees in the 4-dimensional folded hypercube FQ4, and an unused path P consisting of two unused edge-changing paths, the vertex set, edge path set, and unused path P in the two edge-disjoint spanning trees can be expressed as follows:

[0062] The vertex set in the spanning tree of two trees with disjoint edges:

[0063] V(T1)={0,1,□,15}, V(T2)={0,1,□,15};

[0064] The set of edge paths in the edge-disjoint spanning tree of two trees:

[0065] E(T1)={(0,2),(1,5),(2,3),(2,10),(4,6),(5,7),(5,13),(6,14),(8,10),(8,9),(8,12),(11,15),(12,13),(13,15),(14,15)},

[0066] E(T2)={(0,4),(0,8),(1,9),(2,6),(3,7),(3,11),(4,5),(4,12),(6,7),(7,15),(9,11),(9,

[0067] 13),(10,11),(10,14),(12,14)};

[0068] Unused path P:

[0069] P=3-1-0.

[0070] Step 302, when n is greater than 4, based on the two edge-non-intersecting spanning trees and unused paths in the 4-dimensional folded hypercube network, determine the target number of edge-non-intersecting spanning trees in the n-dimensional folded hypercube network through a first construction method and a second construction method; wherein the first construction method is used to determine (m+2) / 2 edge-non-intersecting spanning trees in the m+1-dimensional folded hypercube network through m / 2 edge-non-intersecting spanning trees and unused paths in the m-dimensional folded hypercube network, and the second construction method is used to determine (m+2) / 2 edge-non-intersecting spanning trees in the m+2-dimensional folded hypercube network through m / 2 edge-non-intersecting spanning trees and unused paths in the m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n.

[0071] When n is greater than 4, that is, the present invention is directed to the case where the dimension of the folded hypercube network is ≥5.

[0072] After obtaining two edge-non-intersecting spanning trees and unused paths in a 4-dimensional folded hypercube network, a target number of edge-non-intersecting spanning trees in the n-dimensional folded hypercube network can be determined based on the two edge-non-intersecting spanning trees and unused paths in the 4-dimensional folded hypercube network through a first construction method and a second construction method.

[0073] The first construction method can be used to determine (m+2) / 2 edge-disjoint spanning trees in an m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network.

[0074] The second construction method can be used to determine (m+2) / 2 edge-disjoint spanning trees in an m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network.

[0075] Here, m is an even number greater than or equal to 4 and less than or equal to n.

[0076] In some embodiments of the present invention, the value of the target number is a value obtained by rounding up n / 2, and the value of the number of network nodes in the unused path is a value obtained by rounding up (n+1) / 2.

[0077] That is, the present invention is aimed at the case where the dimension of the folded hypercube network is ≥ 5, and the target number value is the value obtained by rounding up n / 2, which is used to construct the n-dimensional folded hypercube network FQ n At most constructible The target number is the n-dimensional folded hypercube network FQ. n The maximum number of edge-disjoint spanning trees that can be constructed is (n+1) / 2 rounded up to the nearest integer.

[0078] In some embodiments of the present invention, when n is an odd number, determining a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network includes:

[0079] Sub-step 11, based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, recursively execute the second construction method to determine n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1-dimensional folded hypercube network.

[0080] In the n-dimensional folded hypercube network FQ n When constructing an edge-disjoint spanning tree, when n is an odd number, the second construction method can be recursively executed in a loop based on two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network to determine n-1 / 2 (i.e., the target number of n-1 dimensions) edge-disjoint spanning trees and unused paths in an n-1-dimensional folded hypercube network.

[0081] Sub-step 12: executing a first construction method based on the n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1 dimensional folded hypercube network to determine the (n+1) / 2 edge-disjoint spanning trees in the n dimensional folded hypercube network.

[0082] After determining n-1 / 2 edge-disjoint spanning trees and unused paths in an n-1 dimensional folded hypercube network, a first construction method can be executed based on the n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1 dimensional folded hypercube network to determine (n+1) / 2 (i.e., the target number of n dimensions) edge-disjoint spanning trees in the n dimensional folded hypercube network.

[0083] In some embodiments of the present invention, when n is an even number, determining a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network includes:

[0084] Based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, the second construction method is recursively executed to determine n / 2 edge-disjoint spanning trees and unused paths in the n-dimensional folded hypercube network.

[0085] In the n-dimensional folded hypercube network FQ n When constructing an edge-disjoint spanning tree, when n is an even number, the second construction method can be recursively executed in a loop based on two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network to determine n / 2 (i.e., the target number of n dimensions) edge-disjoint spanning trees and unused paths in an n-dimensional folded hypercube network.

[0086] As an example, based on two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network, by executing the second construction method, a target number of two edge-disjoint spanning trees and unused paths in a 6-dimensional folded hypercube network are obtained, and then based on the target number of two edge-disjoint spanning trees and unused paths in the 6-dimensional folded hypercube network, by executing the second construction method, a target number of two edge-disjoint spanning trees and unused paths in an 8-dimensional folded hypercube network can be obtained. Therefore, the second construction method can be combined with recursion to obtain a target number of two edge-disjoint spanning trees in an n-dimensional folded hypercube network based on two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network.

[0087] In some embodiments of the present invention, executing the first construction method includes:

[0088] Sub-step 21, obtaining isomorphic first and second m-dimensional folded hypercube networks, as well as m / 2 edge-disjoint spanning trees and first and second unused paths in the first and second m-dimensional folded hypercube networks, and respectively increasing the highest bit of the binary strings corresponding to the network nodes in the first and second m-dimensional folded hypercube networks to 0 and 1, respectively.

[0089] Obtain an isomorphic first m-dimensional folded hypercube network, a second m-dimensional folded hypercube network, m / 2 edge-disjoint spanning trees and a first used path in the first m-dimensional folded hypercube network, and m / 2 edge-disjoint spanning trees and a second unused path in the second m-dimensional folded hypercube network.

[0090] By adding a highest bit to the binary strings corresponding to the network nodes in the first m-dimensional folded hypercube network and the second m-dimensional folded hypercube network and setting them to 0 and 1 respectively, the topological structures corresponding to the isomorphic first m-dimensional folded hypercube network and the second m-dimensional folded hypercube network can be used as two isomorphic subgraphs of the m+1-dimensional folded hypercube network, that is, and

[0091] Two subgraphs A and B are isomorphic. In subgraph A, we get m / 2 edge-disjoint spanning trees. In subgraph B, we also get m / 2 edge-disjoint spanning trees. And the trees in subgraph B are isomorphic to the trees in subgraph A. Therefore, we can find a specific solution to convert and By connecting every two trees in m+1 In Edge-disjoint spanning trees (EDSTs).

[0092] Sub-step 22, connecting the isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the first and second m-dimensional folded hypercube networks respectively through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the first and second unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network.

[0093] Through the previous step, you can get There are m / 2 edge-disjoint spanning trees EDSTs (plural form of EDST): is (m+1) / 2 rounded down, that is, m / 2. The m / 2 edge-disjoint spanning trees EDSTs in: In addition to In addition to the edges contained in the m / 2 EDST trees, The remaining edge paths in the A : That is, the first unused path; similarly, except In addition to the edges contained in the m / 2 EDST trees, An unused path P in B : That is the second unused path.

[0094] Then, the isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the first m-dimensional folded hypercube network and the second m-dimensional folded hypercube network can be connected respectively through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the first used path and the second unused path to obtain the first m / 2-1 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network.

[0095] Specifically, you can make Depend on connect and T can be constructed i , that is, V(T i )←V(FQ m+1 ), In this way, FQ can be completed m+1 The front The construction of EDSTs can obtain the first m / 2-1 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network.

[0096] Sub-step 23, connecting the network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the m-th edge of each network node in the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the first m edge paths in the second unused paths, to obtain the m / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network; wherein the m-th edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth bit.

[0097] First of all, it should be noted that if the binary strings of vertex (i.e. network node) x and vertex y differ only in the i-th bit, (x, y) is called the i-th edge of x.

[0098] Furthermore, for the m / 2th edge-non-intersecting spanning tree in the m+1-dimensional folded hypercube network, the network nodes in the m / 2th edge-non-intersecting spanning tree in the second m-dimensional folded hypercube network can be connected to the m / 2th edge-non-intersecting spanning tree in the first m-dimensional folded hypercube network through the m-dimensional edge of each network node in the m / 2th edge-non-intersecting spanning tree in the first m-dimensional folded hypercube network.

[0099] Then, through the first m edge paths in the second unused path, the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network are connected to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network to obtain the m / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network.

[0100] Specifically, FQ m+1 The m / 2th EDST in first contains Spanning tree in Then you can The m-dimensional edge of each vertex in The vertices in are connected to On, because the vertex The m-th edge of has been used in the first m / 2-1 EDSTs, so There are still some vertices not connected to Finally, we can use path P B The edge Connect the remaining vertices in B to , where m / 2≥j≥1. So far, FQ m+1 The construction of the m / 2th EDSTs in is completed.

[0101] Sub-step 24, complementing the binary string corresponding to each network node in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to obtain the corresponding network node in the first m-dimensional folded hypercube network, and connecting it to the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network.

[0102] Specifically, for FQ m+1 The last edge-disjoint spanning tree in The binary string corresponding to each network node in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network can be complemented to obtain the corresponding network node in the first m-dimensional folded hypercube network, and connected to the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network. Complement each vertex in and connect it to To obtain FQ m+1 The last edge-disjoint spanning tree in

[0103] Based on the above steps, the Figure 4 The first construction method shown obtains (m+2) / 2 edge-disjoint spanning trees in the m+1 dimensional folded hypercube network.

[0104] In some embodiments of the present invention, executing the second construction method includes:

[0105] Sub-step 31, obtaining isomorphic third, fourth, fifth, and sixth m-dimensional folded hypercube networks, as well as m / 2 edge-disjoint spanning trees and third, fourth, fifth, and sixth unused paths in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks, and respectively increasing the two highest bits of the binary strings corresponding to the network nodes in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks to 00, 10, 11, and 01, respectively.

[0106] Obtain isomorphic third m-dimensional folded hypercube network, fourth m-dimensional folded hypercube network, fifth m-dimensional folded hypercube network, and sixth m-dimensional folded hypercube network, as well as m / 2 edge-disjoint spanning trees and third unused paths, fourth unused paths, fifth unused paths, and sixth unused paths in the third m-dimensional folded hypercube network, fourth m-dimensional folded hypercube network, fifth m-dimensional folded hypercube network, and sixth m-dimensional folded hypercube network.

[0107] And by respectively adding two highest bits to the binary strings corresponding to the network nodes in the third m-dimensional folded hypercube network, the fourth m-dimensional folded hypercube network, the fifth m-dimensional folded hypercube network, and the sixth m-dimensional folded hypercube network, respectively, and setting them to 00, 10, 11, and 01, then the topological structures corresponding to the isomorphic third m-dimensional folded hypercube network, the fourth m-dimensional folded hypercube network, the fifth m-dimensional folded hypercube network, and the sixth m-dimensional folded hypercube network can be used as four isomorphic subgraphs of the m+2-dimensional folded hypercube network, that is,

[0108] The four subgraphs A, B, C, and D are isomorphic. In subgraph A, we get m / 2 edge-disjoint spanning trees. In subgraphs B, C, and D, we can also get m / 2 edge-disjoint spanning trees. The trees in subgraphs B, C, and D are isomorphic to the trees in subgraph A. Therefore, we can find a specific solution to convert and By connecting every two trees in m+2 In Edge-disjoint spanning trees (EDSTs).

[0109] Sub-step 32, respectively connecting the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the third and fourth m-dimensional folded hypercube networks through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the third and fourth unused paths, respectively connecting the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the fourth and fifth unused paths, and respectively connecting the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks through the edge paths formed by connecting the first m / 2-1 network nodes at the same position in the fifth and sixth unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network.

[0110] Through the previous step, you can get There are m / 2 edge-disjoint spanning trees EDSTs (plural form of EDST): The m / 2 edge-disjoint spanning trees EDSTs in: In addition to In addition to the edges contained in the m / 2 EDST trees, The remaining edge paths in the A : That is, the first unused path; similarly, except In addition to the edges contained in the m / 2 EDST trees, An unused path P in B : That is, the second unused path. Similarly, we can also get and The path P in C and P D .

[0111] Then, the isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the third unused path and the fourth m-dimensional folded hypercube network can be connected respectively through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the third unused path and the fourth unused path.

[0112] The isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth unused path and the fifth m-dimensional folded hypercube network can be connected respectively through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the fourth unused path and the fifth unused path.

[0113] Furthermore, the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the fifth unused path and the sixth m-dimensional folded hypercube network can be connected respectively through the edge paths formed by connecting the first m / 2-1 network nodes at the same position in the fifth unused path and the sixth unused path, so as to obtain the first m / 2-1 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network.

[0114] Specifically, let m / 2-1≥i≥1, then connect and Depend on connect and Depend on connect and T can be constructed i , that is, V(T i )←V(FQ m+2 ),

[0115] So far, FQ m+2 The construction of the first m / 2-1 EDSTs is completed.

[0116] Sub-step 33, connecting the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fourth and fifth unused paths, connecting the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fifth and sixth unused paths, connecting all network nodes in the third m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-dimensional edges of all network nodes in the third m-dimensional folded hypercube network, and obtaining the m / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network; wherein the m-dimensional edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth position.

[0117] First of all, it should be noted that the vertex (i.e., network node) y = (x, N x,i ) means that the binary strings of vertex x and vertex y differ only in the i-th position, that is, y is the i-th edge of x, then we use Representing a subgraph The m-th edge of all vertices in .

[0118] Furthermore, for the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network, first, the m / 2th edge-disjoint spanning tree that is isomorphic to the m / 2th edge-disjoint spanning tree in the fourth unused path and the fifth m-dimensional folded hypercube network can be connected through the edge path formed by the m / 2th network node at the same position in the fourth unused path and the fifth unused path.

[0119] Secondly, the m / 2th edge-disjoint spanning tree that is isomorphic to the m / 2 edge-disjoint spanning trees in the fifth unused path and the sixth m-dimensional folded hypercube network can be connected through the edge path formed by the m / 2th network node at the same position in the fifth unused path and the sixth unused path.

[0120] Then, all network nodes in the third m-dimensional folded hypercube network can be connected to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-dimensional edges of all network nodes in the third m-dimensional folded hypercube network to obtain the m / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network.

[0121] Specifically, FQ m+2 The m / 2th edge-disjoint spanning tree EDST in the first contains FQm+2 Three subgraphs of and The three spanning trees in and Then you can pass through the edge Will and Connect, through the edge Will and Finally, you can use Subgraph All vertices in the At this point, FQ + The construction of the m / 2th EDSTs in is completed.

[0122] Sub-step 34, connecting the network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through all edge paths in the fourth unused path.

[0123] For the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network, that is, the last edge-disjoint spanning tree, this step and the subsequent sub-steps 35 and 36 can be used to complete the construction.

[0124] The network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network can be connected to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network, and the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network can be connected to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through all edge paths in the fourth unused path.

[0125] Specifically, FQ m+2 The (m+2) / 2th EDST in first contains Spanning tree in Then you can The m+1-dimensional edge of each vertex (i.e., network node) in The vertices in are connected to On, because the vertex The m+1th edge of has been used in the first m / 2 EDSTs, so There are still some vertices not connected to Finally, we can use path P B All edges in The remaining vertices in are connected to middle.

[0126] Sub-step 35, connecting the network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-th edge of each network node in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through all edge paths in the fourth unused path.

[0127] After step 34 is completed, step 35 is similar to the process in step 34. Specifically, by The m-dimensional edge of each vertex in The vertices in are connected to and use path P C All edges in The remaining vertices in are connected to middle.

[0128] Sub-step 36, connecting the network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through all edge paths in the sixth unused path, to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network.

[0129] After step 35 is completed, step 36 is similar to the process in steps 34 and 35. Specifically, by The m+1-dimensional edge of each vertex in The vertices in are connected to and use path P D All edges in The remaining vertices in are connected to middle.

[0130] Then the m+2 dimensional folded hypercube network FQ is completed m+2 The last one, i.e., the (m+2) / 2th edge-disjoint spanning tree, that is, the construction of the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network is completed through steps 34, 35, and 36.

[0131] Sub-step 37, obtaining unused paths in the m+2-dimensional folded hypercube network based on the (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network.

[0132] In order to facilitate the recursive call of the second construction method, the construction of the edge-non-intersecting spanning trees in the subsequent m+4-dimensional folded hypercube network can be based on the (m+2) / 2 edge-non-intersecting spanning trees in the m+2-dimensional folded hypercube network to obtain the unused paths in the m+2-dimensional folded hypercube network.

[0133] Based on the above steps, the second construction method is completed, and the (m+2) / 2 edge-disjoint spanning trees and unused paths in the m+2-dimensional folded hypercube network are obtained.

[0134] Step 303, completing the 2 n Communication between any two of the network nodes.

[0135] In obtaining the n-dimensional folded hypercube network FQ n In After the edge-disjoint spanning tree, the n-dimensional folded hypercube network FQ n 2 of 2 n Any two network nodes in the network nodes can be connected through the n-dimensional folded hypercube network FQ n In The paths corresponding to the edge-disjoint spanning trees are used for communication.

[0136] In practical applications, all edge-disjoint spanning trees EDSTs (plural form of EDST) that can be constructed in the output folded hypercube network can be further obtained to obtain all edge-disjoint paths between any two network nodes in the folded hypercube network.

[0137] For diagnosing faults in the network, there are a large number of routers, processors, switches, links, etc. in large-scale / clustered interconnected networks, and each node or link may fail. If there are multiple non-intersecting communication links between any two nodes in this network, then occasional faults or even small-scale faults will affect the data transmission between the two nodes to a small extent. In addition, relying on the construction algorithm of the edge-disjoint spanning tree in the network, we can further explore the fault diagnosis algorithm in the network.

[0138] Specifically, the n non-intersecting paths between two network nodes are each responsible for sending 1 / n copies of the information, so only the starting point and the end point can obtain complete information, ensuring the security of the information; the n non-intersecting paths between two network nodes can still communicate normally in the presence of n-1 faulty links, and the same is true for broadcasting, which helps to improve the fault tolerance of communication / broadcasting; the same instance of the same algorithm that can be used to resist man-in-the-middle attacks can be run in n edge-non-intersecting spanning trees. If the n running results of the same instance are different, the occurrence of a man-in-the-middle attack can be confirmed and located.

[0139] In an embodiment of the present invention, by obtaining two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network, when n is greater than 4, based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network is determined through a first construction method and a second construction method. The first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in an m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network. The second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in an m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n. The 2 is completed through the target number of edge-disjoint spanning trees. n The invention realizes the communication between any two of the network nodes, realizes the construction of all edge-disjoint spanning trees in the n-dimensional folded hypercube network, enables the network nodes to communicate through multiple paths, improves the fault tolerance of communication in the folded hypercube network, and the security of information transmission, and can also be applied to the distributed algorithm for resisting man-in-the-middle attacks to confirm and locate the occurrence of man-in-the-middle attacks.

[0140] It should be noted that, for the sake of simplicity, the method embodiments are described as a series of action combinations, but those skilled in the art should be aware that the embodiments of the present invention are not limited by the order of the actions described, because according to the embodiments of the present invention, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions involved are not necessarily required by the embodiments of the present invention.

[0141] Reference Figure 5 , showing a schematic diagram of the structure of a communication device based on a folded hypercube network provided by some embodiments of the present invention, applied to an n-dimensional folded hypercube network, wherein the n-dimensional folded hypercube network includes 2 n network nodes, acyclic paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree, paths between two adjacent network nodes form edge paths, multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network form unused paths, n is an integer greater than or equal to 4, and may specifically include the following modules:

[0142] A four-dimensional spanning tree acquisition module 501, used to acquire two edge-disjoint spanning trees and unused paths in a four-dimensional folded hypercube network;

[0143] The n-dimensional spanning tree construction module 502 is used to determine the target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network when n is greater than 4; wherein the first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network by m / 2 edge-disjoint spanning trees and unused paths in the m-dimensional folded hypercube network, and the second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network by m / 2 edge-disjoint spanning trees and unused paths in the m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n;

[0144] Path module 503, used to complete the above 2 by generating trees without intersecting edges of the target number. n Communication between any two of the network nodes.

[0145] In one embodiment of the present invention, the n-dimensional folded hypercube network has 2 n Each network node is represented by a binary string of length n.

[0146] In one embodiment of the present invention, the value of the target number is a value obtained by rounding up n / 2, and the value of the number of network nodes in the unused path is a value obtained by rounding up (n+1) / 2.

[0147] In one embodiment of the present invention, when n is an odd number, the n-dimensional spanning tree construction module 502 includes:

[0148] A first recursive calling submodule is used to recursively execute the second construction method based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network to determine n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1-dimensional folded hypercube network;

[0149] The first construction submodule is used to execute a first construction method based on the n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1 dimensional folded hypercube network to determine the (n+1) / 2 edge-disjoint spanning trees in the n-dimensional folded hypercube network.

[0150] In one embodiment of the present invention, when n is an even number, the n-dimensional spanning tree construction module 502 includes:

[0151] The second recursive calling submodule is used to recursively execute the second construction method based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network to determine n / 2 edge-disjoint spanning trees and unused paths in the n-dimensional folded hypercube network.

[0152] In one embodiment of the present invention, the first construction submodule includes:

[0153] an acquisition unit, used for acquiring isomorphic first and second m-dimensional folded hypercube networks, and m / 2 edge-disjoint spanning trees and first and second unused paths in the first and second m-dimensional folded hypercube networks, and respectively increasing a highest bit of the binary strings corresponding to the network nodes in the first and second m-dimensional folded hypercube networks, and setting them to 0 and 1 respectively;

[0154] A first construction unit connects the isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the first and second m-dimensional folded hypercube networks respectively through edge paths formed by connecting the first m / 2-2 network nodes at the same position in the first and second unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network;

[0155] a second construction unit, configured to connect the network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the m-th edge of each network node in the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network, and to connect the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the first m edge paths in the second unused paths, so as to obtain the m / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network; wherein the m-th edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth bit;

[0156] The third construction unit is used to complement the binary string corresponding to each network node in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to obtain the corresponding network node in the first m-dimensional folded hypercube network, and connect it to the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network.

[0157] In one embodiment of the present invention, the first recursive calling submodule and the second recursive calling submodule include:

[0158] A second acquisition unit is used to acquire isomorphic third, fourth, fifth, and sixth m-dimensional folded hypercube networks, and m / 2 edge-disjoint spanning trees and third, fourth, fifth, and sixth unused paths in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks, and respectively increase two highest bits of the binary strings corresponding to the network nodes in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks to 00, 10, 11, and 01, respectively;

[0159] a fourth construction unit, configured to respectively connect the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the third and fourth m-dimensional folded hypercube networks through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the third and fourth unused paths, respectively connect the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the fourth and fifth unused paths, and respectively connect the m / 2-1 edge-disjoint spanning trees that are isomorphic to the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks through the edge paths formed by connecting the first m / 2-1 network nodes at the same position in the fifth and sixth unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network;

[0160] a fifth construction unit, configured to connect the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fourth and fifth unused paths, connect the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fifth and sixth unused paths, connect all network nodes in the third m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-dimensional edges of all network nodes in the third m-dimensional folded hypercube network, and obtain the m / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network; wherein the m-dimensional edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth position;

[0161] a first connection unit, configured to connect the network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network, and to connect the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through all edge paths in the fourth unused path;

[0162] a second connection unit, configured to connect the network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-th edge of each network node in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network, and to connect the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through all edge paths in the fourth unused path;

[0163] a third connecting unit, configured to connect the network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network, and to connect the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through all edge paths in the sixth unused path, so as to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network;

[0164] The unused path acquisition unit is used to obtain unused paths in the m+2 dimensional folded hypercube network based on (m+2) / 2 edge-disjoint spanning trees in the m+2 dimensional folded hypercube network.

[0165] In an embodiment of the present invention, by obtaining two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network, when n is greater than 4, based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network is determined through a first construction method and a second construction method. The first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in an m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network. The second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in an m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in an m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n. The 2 is completed through the target number of edge-disjoint spanning trees. nThe invention realizes the communication between any two of the network nodes, realizes the construction of all edge-disjoint spanning trees in the n-dimensional folded hypercube network, enables the network nodes to communicate through multiple paths, improves the fault tolerance of communication in the folded hypercube network, and the security of information transmission, and can also be applied to the distributed algorithm for resisting man-in-the-middle attacks to confirm and locate the occurrence of man-in-the-middle attacks.

[0166] Some embodiments of the present invention further provide an electronic device, comprising a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the above method is implemented when the computer program is executed by the processor.

[0167] Some embodiments of the present invention further provide a computer-readable storage medium, on which a computer program is stored, and the computer program implements the above method when executed by a processor.

[0168] Some embodiments of the present invention further provide a computer program product, including a computer program, which implements the above method when executed by a processor.

[0169] As for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0170] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with the relevant laws, regulations and standards of the relevant countries and regions, and provide corresponding operation entrances for users to choose to authorize or refuse.

[0171] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0172] Those skilled in the art will appreciate that the embodiments of the present invention may be provided as methods, devices, or computer program products. Therefore, the embodiments of the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the embodiments of the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0173] The embodiments of the present invention are described with reference to the flowcharts and / or block diagrams of the methods, terminal devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing terminal device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing terminal device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0174] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing terminal device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0175] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal device so that a series of operating steps are executed on the computer or other programmable terminal device to produce a computer-implemented process, thereby providing instructions for executing on the computer or other programmable terminal device to implement the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0176] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the embodiments of the present invention.

[0177] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal device. In the absence of further restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the process, method, article or terminal device including the above elements.

[0178] The above is a detailed introduction to a communication method and device based on a folded hypercube network. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A communication method based on a folded hypercube network, characterized in that: Applied to an n-dimensional folded hypercube network, the n-dimensional folded hypercube network comprising 2 n network nodes, acyclic paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree, paths between two adjacent network nodes form edge paths, and multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network form unused paths, the method comprising: Get two edge-disjoint spanning trees and unused paths in a 4-dimensional folded hypercube network; In the case where n is greater than 4, based on the two edge-disjoint spanning trees and the unused paths in the 4-dimensional folded hypercube network, a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network are determined by a first construction method and a second construction method; wherein the first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and the unused paths in the m-dimensional folded hypercube network, and the second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and the unused paths in the m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n; By constructing a non-intersecting tree with the target number of edges, the above 2 n Communication between any two of the network nodes.

2. The method according to any one of claim 1, characterized in that: The n-dimensional folded hypercube network 2 n Each network node is represented by a binary string of length n.

3. The method according to claim 2, characterized in that The value of the target number is a value obtained by rounding up n / 2, and the value of the number of network nodes in the unused path is a value obtained by rounding up (n+1) / 2.

4. The method according to claim 3, characterized in that: When n is an odd number, the method of determining a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network comprises: Based on the two edge-disjoint spanning trees and the unused paths in the 4-dimensional folded hypercube network, recursively executing the second construction method to determine n-1 / 2 edge-disjoint spanning trees and the unused paths in the n-1-dimensional folded hypercube network; Based on the n-1 / 2 edge-disjoint spanning trees and unused paths in the n-1 dimensional folded hypercube network, a first construction method is executed to determine (n+1) / 2 edge-disjoint spanning trees in the n dimensional folded hypercube network.

5. The method according to claim 3, characterized in that: When n is an even number, the method of determining a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network by a first construction method and a second construction method based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network includes: Based on the two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network, the second construction method is recursively executed to determine n / 2 edge-disjoint spanning trees and unused paths in the n-dimensional folded hypercube network.

6. The method according to claim 4, characterized in that The executing the first construction method comprises: Obtaining isomorphic first and second m-dimensional folded hypercube networks, as well as m / 2 edge-disjoint spanning trees and first and second unused paths in the first and second m-dimensional folded hypercube networks, and respectively increasing a highest bit of the binary strings corresponding to the network nodes in the first and second m-dimensional folded hypercube networks to 0 and 1, respectively; Connecting the isomorphic m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the first and second m-dimensional folded hypercube networks respectively through the edge paths formed by connecting the first m / 2-2 network nodes at the same position in the first and second unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network; The network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network are connected to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the m-th edge of each network node in the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network, and the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network are connected to the m / 2th edge-disjoint spanning tree in the first m-dimensional folded hypercube network through the first m edge paths in the second unused path, so as to obtain the m / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network; wherein the m-th edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth bit; The binary string corresponding to each network node in the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network is complemented to obtain the corresponding network node in the first m-dimensional folded hypercube network, and connected to the m / 2th edge-disjoint spanning tree in the second m-dimensional folded hypercube network to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+1-dimensional folded hypercube network.

7. The method according to any one of claims 4 to 5, characterized in that: The executing the second construction method comprises: Obtaining isomorphic third, fourth, fifth, and sixth m-dimensional folded hypercube networks, as well as m / 2 edge-disjoint spanning trees and third, fourth, fifth, and sixth unused paths in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks, and respectively increasing the two highest bits of the binary strings corresponding to the network nodes in the third, fourth, fifth, and sixth m-dimensional folded hypercube networks to 00, 10, 11, and 01, respectively; The first m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the third and fourth m-dimensional folded hypercube networks are respectively connected through the edge paths formed by connecting the first m / 2-2 network nodes in the same position in the third and fourth unused paths, the first m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks are respectively connected through the edge paths formed by connecting the first m / 2-2 network nodes in the same position in the fourth and fifth unused paths, and the first m / 2-1 edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks are respectively connected through the edge paths formed by connecting the first m / 2-1 network nodes in the same position in the fifth and sixth unused paths, to obtain the first m / 2-1 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network; Connecting the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fourth and fifth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fourth and fifth unused paths, connecting the isomorphic m / 2th edge-disjoint spanning trees in the m / 2 edge-disjoint spanning trees in the fifth and sixth m-dimensional folded hypercube networks through the edge path formed by the m / 2th network node at the same position in the fifth and sixth unused paths, connecting all network nodes in the third m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-dimensional edges of all network nodes in the third m-dimensional folded hypercube network, and obtaining the m / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network; wherein the m-dimensional edge of the network node is an edge path formed by the network node and another network node, and the binary strings corresponding to the network node and the another network node differ only in the mth position; Connecting the network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the third m-dimensional folded hypercube network through all edge paths in the fourth unused path; Connecting the network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through the m-th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fourth m-dimensional folded hypercube network through all edge paths in the fourth unused path; Connecting the network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through the m+1th dimensional edge of each network node in the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network, and connecting the unconnected network nodes in the m / 2th edge-disjoint spanning tree in the sixth m-dimensional folded hypercube network to the m / 2th edge-disjoint spanning tree in the fifth m-dimensional folded hypercube network through all edge paths in the sixth unused path, to obtain the (m+2) / 2th edge-disjoint spanning tree in the m+2-dimensional folded hypercube network; Based on (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network, unused paths in the m+2-dimensional folded hypercube network are obtained.

8. A communication device based on a folded hypercube network, characterized in that: Applied to an n-dimensional folded hypercube network, the n-dimensional folded hypercube network comprising 2 n network nodes, acyclic paths connecting all network nodes in the n-dimensional folded hypercube network form a spanning tree, paths between two adjacent network nodes form edge paths, multiple unused edge paths in all edge-disjoint spanning trees in the n-dimensional folded hypercube network form unused paths, n is an integer greater than or equal to 4, and the device comprises: A four-dimensional spanning tree acquisition module, used to obtain two edge-disjoint spanning trees and unused paths in a four-dimensional folded hypercube network; An n-dimensional spanning tree construction module is used to determine a target number of edge-disjoint spanning trees in the n-dimensional folded hypercube network based on two edge-disjoint spanning trees and unused paths in the 4-dimensional folded hypercube network through a first construction method and a second construction method when n is greater than 4; wherein the first construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+1-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in the m-dimensional folded hypercube network, and the second construction method is used to determine (m+2) / 2 edge-disjoint spanning trees in the m+2-dimensional folded hypercube network through m / 2 edge-disjoint spanning trees and unused paths in the m-dimensional folded hypercube network, where m is an even number greater than or equal to 4 and less than or equal to n; A path module is used to generate a tree without intersection through the target number of edges to complete the 2 n Communication between any two of the network nodes.

9. An electronic device, characterized in that: The invention comprises a processor, a memory and a computer program stored in the memory and capable of running on the processor, wherein when the computer program is executed by the processor, the communication method based on the folded hypercube network as claimed in any one of claims 1 to 7 is implemented.

10. A readable storage medium, characterized in that: The readable storage medium stores a computer program, and when the computer program is executed by a processor, the communication method based on a folded hypercube network as claimed in any one of claims 1 to 7 is implemented.

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