Parallel transmission method for data on interconnection network based on 3-element n-cube

Abstract

The invention belongs to the technical field of communication, and discloses a parallel transmission method for data on an interconnection network based on a 3-element n-cube, and (n-1)! Is found according to the dimension n of the 3-element n-cube. The method comprises the following steps: determining nodes x, grouping circles, gradually establishing independent spanning trees according to each group of circle arrangements and the determined node x, generating independent spanning trees of different groups according to different circle arrangements, enabling the independent spanning trees of different groups to correspond to disjoint paths of different groups, finding out a group of optimal disjoint paths according to different circle arrangements, and carrying out data parallel transmission. According to the method, the communication overhead can be remarkably reduced, meanwhile, the balance of the communication cost is optimized, huge market potential is shown in wide application of an interconnection network structure, and an efficient and reliable solution is provided for a high-performance computing and large-scale parallel system.

Description

Technical Field

[0001] The invention belongs to the field of communication technology, and in particular relates to a parallel transmission method for data on a 3-element n-cube structure interconnection network. Background Art

[0002] The rapid development of artificial intelligence technology has put forward unprecedented demands for high performance computing (HPC), driving the continuous growth of computing resources. As a core research tool for achieving major scientific breakthroughs, HPC mainly relies on parallel and distributed systems, in which the design and performance of the interconnection network plays a decisive role. The interconnection network is usually described by a graph theory model, in which processors are abstracted as vertices and the communication links between processors are represented as edges. In this context, the hypercube, as a classic interconnection network topology, is highly favored for its low latency, high symmetry, good scalability and recursive characteristics. However, the hypercube structure also has certain limitations: as the network dimension increases, the degree of the node also increases. This increase in node degree may bring additional complexity to the parallel computing system, such as higher hardware cost and communication overhead, thus becoming a potential challenge in system design.

[0003] 3-ary n-cube ) is an important extension of the hypercube and an excellent interconnected network topology. While inheriting the core advantages of the hypercube such as low latency, high symmetry and scalability, it further introduces new features such as reducing message transmission latency and simplifying hardware implementation, making it show significant application value in the fields of parallel computing and supercomputers. With the continuous deepening of interconnected network research, the application of its construction strategy in data center networks has also shown broad prospects, providing new solutions for improving the efficiency and reliability of large-scale data processing.

[0004] In an interconnected network based on a 3-ary n-cube topology network, as the scale of processors increases, it is particularly important to quickly construct multiple point-disjoint links to achieve efficient parallel data transmission. When the source processor needs to transmit large amounts of data to the target processor, these point-disjoint links can be implemented through vertex independent spanning trees (ISTs). Specifically, for a given network, a vertex independent spanning tree refers to a set of spanning trees that share the same root node, and the path from the root node to any other node does not share any vertices except the root node in all spanning trees. However, the existing method for constructing point independent spanning trees in 3-ary n-cube networks mainly relies on a serial recursive algorithm, which has a high time complexity and is difficult to meet the high efficiency requirements of large-scale networks. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a parallel transmission method for data on a 3-ary n-cube structured interconnection network. For any given vertex, the method can construct 2n point-independent spanning trees in parallel, and each tree can be constructed independently. At the same time, it is ensured that there are 2n point-disjoint paths between the root node and any other node in the network.

[0006] In order to achieve the above object, the present invention is achieved through the following technical solutions:

[0007] The present invention is a parallel data transmission method on an interconnection network based on a 3-element n-cube. In a multiprocessor system based on a 3-element n-cube structure interconnection network, a source node is a sender of data, a destination node is a receiver of data, and the edge between the source node and the destination node is a physical link or a virtual link to realize data transmission. A point-to-point independent spanning tree is constructed with the source node as the root node to obtain multiple groups of non-intersecting paths, thereby reducing transmission time, reducing communication delay, and enhancing the fault tolerance of data transmission. Data is transmitted on a 3-element n-cube structure interconnection network, wherein the dimension of the 3-element n-cube structure is n, the connectivity is 2n, and the source node is x=x n x n-1 …x1, build 2n independent spanning trees based on the source node and use it as the root. Any vertex v is represented by an n-bit triple: v = v n-1 v n-2 …v0. In order to better represent the relationship between points, the present invention uses N ± (v,i) represents two adjacent points of point v. They are N + (v,i)=v n-1 v n-2 …(v i +1)mod3…v0,N - (v,i)=v n-1 v n-2 …(v i -1)mod3…v0; The method for constructing 2n independent spanning trees, each with a height of n+1, i.e., the method for parallel data transmission, comprises the following steps:

[0008] Step 1: Set the source node x=x n x n-1 …x1 is fixed as the root node of the independent spanning tree. According to the dimension n of the 3-tuple n-cube, find (n-1)! The circular permutation CDP is represented by an n-bit triple, that is, CDP = a n-1 a n-2 …a0;

[0009] Step 2: Build the first independent spanning tree and the second independent spanning tree: Find the a of the source node x n-1 The two-dimensional adjacent points of are used as the first independent spanning tree and the second independent spanning tree with the source node x as the only child node of the root node, and then the following nodes are gradually established according to the circle arrangement CDP;

[0010] Step 3: Establish the 2i-1th independent spanning tree and the 2ith independent spanning tree, 1<i<n-1, specifically: select a of the source node x n-i The two dimensional adjacent points of the dimension are used as the only child nodes of the root of the 2i-1th independent spanning tree and the 2ith independent spanning tree, and the subsequent nodes are gradually established according to the given circle arrangement CDP;

[0011] Step 4: Establish the 2n-1th independent spanning tree and the 2nth independent spanning tree, i.e., the last two independent spanning trees, find the adjacent points of the source node x in dimension a0, and then gradually establish the nodes of the spanning tree except the critical points of the source node x in dimension a0 according to the given circle arrangement;

[0012] Step 5: According to different arrangements of circles, find a set of optimal non-intersecting paths for parallel data transmission.

[0013] A further improvement of the present invention is that: in the step 1, according to the dimension n of the 3-dimensional n-cube, find (n-1)! The circular arrangement CDP=a n-1 a n-2 …a1 specifically includes the following steps:

[0014] Step 1.1, determine the element set: generate a set S = {0, 1, 2, ..., n-1} containing n elements;

[0015] Step 1.2: Generate a linear permutation without considering cyclic permutations. For n elements, the total number of linear permutations is the factorial of n.

[0016] Step 1.3: For each linear permutation, fix one element and then generate all possible permutations. For each linear permutation, after fixing one element, the remaining elements generate a circular permutation. The total number of circular permutations is (n-1)!

[0017] A further improvement of the present invention is that step 2 specifically comprises the following steps:

[0018] Step 2.1, build the first independent spanning tree T1 and the second independent spanning tree T2, find the source node x's a n-1 Two adjacent points of dimension:

[0019]

[0020] Among them, N + (x,a n-1 ) and N + (x,a n-1 ) are the only child nodes of the root nodes of the first independent spanning tree and the second independent spanning tree respectively;

[0021] Step 2.2, put the only child node of the first independent spanning tree T1 in the set V(T1), and put the only child node of the second independent spanning tree T2 in the set V(T2), at this time V(T1) = {y1}, V(T2) = {y2};

[0022] Step 2.3, establish the following nodes layer by layer: in the first layer, find the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2), connect the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) with the points in the sets V(T1) and V(T2) to form edges, add the edges to the sets E(T1) and E(T2) storing the edges of the first independent spanning tree T1 and the second independent spanning tree T2, add the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) to the sets V(T1) and V(T2). V(T2); in the second layer, find the a1-dimensional adjacent points in the sets V(T1) and V(T2), connect the a1-dimensional adjacent points of the points in the sets V(T1) and V(T2) with the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) to form edges, add the edges to the sets E(T1) and E(T2), and add the a1-dimensional adjacent points in the sets V(T1) and V(T2) in the second layer to the sets V(T1) and V(T2); in the nth layer, find the a1-dimensional adjacent points in the sets V(T1) and V(T2) n-1 dimensional adjacent points, and the n-th layer set V(T1) and the set V(T2) in a n-1 The a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) are connected to form edges, and the edges are added to the sets E(T1) and E(T2). The a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) are added to the sets V(T1) and V(T2). At this time, the first independent spanning tree T1 and the second independent spanning tree T2 are established.

[0023] A further improvement of the present invention is that step 3 specifically comprises the following steps:

[0024] Step 3.1, build the 2i-1th independent spanning tree and the 2ith independent spanning tree, and find the root node x's a n-i Two adjacent points of dimension:

[0025]

[0026]

[0027] Among them, N + (x,a n-i ) and N - (x,a n-i ) are the only child nodes of the root nodes of the 2i-1th independent spanning tree and the 2ith independent spanning tree respectively; according to the circle arrangement, the following nodes are established layer by layer;

[0028] Step 3.2: The 2i-1th independent spanning tree T 2i-1 The only child node is placed in the 2i-1th independent spanning tree T 2i-1 The set of points V(T 2i-1 ), the 2ith independent spanning tree T 2i The only child node is placed in the 2ith independent spanning tree T 2i The set of points V(T 2i ), at this time V(T 2i-1 )={y 2i-1},V(T 2i )={y 2i};

[0029] Step 3.3, build the following nodes layer by layer: In the first layer, find the set V(T 2i-1 ) and the set V(T 2i ) midpoint a (n-i-1)mod n dimensional adjacent points, the set V(T 2i-1 ) and the set V(T 2i ) midpoint a (n-i-1)mod n The adjacent points of the dimension and the set V(T 2i-1 ) and the set V(T 2i ) to form an edge, and add the edge to store the 2i-1th independent spanning tree T 2i-1 The edge set E(T 2i-1 ) and store the 2ith independent spanning tree T 2i The edge set E(T 2i ), the set V(T 2i-1 ) and the set V(T 2i ) midpoint a (n-i-1)mod n The adjacent points of dimension are added to the set V(T 2i-1 ) and the set V(T 2i ), in the second layer, find the set V(T 2i-1 ) and the set V(T 2i ) (n-i-2)mod n dimensional adjacent points, will be set in the second layer V(T 2i-1 ) and the set V(T 2i ) (n-i-2)mod n dimensional adjacent points and set V(T 2i-1) and the set V(T 2i ) to form an edge, and add the edge to the set E(T 2i-1 ) and the set E(T 2i ), the set V(T 2i-1 ) and the set V(T 2i ) (n-i-2)mod n The adjacent points are added to the set V(T 2i-1 ) and the set V(T 2i ), in the next layer, find the set V(T 2i-1 ) and the set V(T 2i ) (n-i-3)mod n The adjacent points are thus established until the nth layer, and the set V(T 2i-1 ) and the set V(T 2i ) n-i dimensional adjacent points, the n-th layer set V(T 2i-1 ) and the set V(T 2i ) n-i dimensional adjacent points and the set E(T 2i-1 ) and the set E(T 2i ) to form an edge, and add the edge to the set E(T 2i-1 ) and the set E(T 2i ), the n-th layer set V(T 2i-1 ) and the set V(T 2i ) n-i The adjacent points are added to the set V(T 2i-1 ) and the set V(T 2i ), at this time, the 2i-1th independent spanning tree T 2i-1 and the 2ith independent spanning tree T 2i Complete the build.

[0030] A further improvement of the present invention is that step 4 specifically includes the following steps:

[0031] Step 4.1. Establish the 2n-1th independent spanning tree and the 2nth independent spanning tree, and find the two adjacent points of the root node x in dimension a0:

[0032]

[0033] Among them, N + (x,a0) is the only child node of the 2n-1th independent spanning tree, N - (x,a0) is the only child node of the 2nth independent spanning tree;

[0034] Step 4.2: The 2n-1th independent spanning tree T 2n-1 The only child node is placed in the set V(T 2n-1), the 2nth independent spanning tree T 2n The only child node is placed in the set V(T 2n ), at this time V(T 2n-1 )={y 2n-1},V(T 2n )={y 2n};

[0035] Step 4.3, build the following nodes layer by layer: In the first layer, find the set V(T 2n-1 ) and the set V(T 2n ) midpoint a n-1 dimensional adjacent points, the set V(T 2n-1 ) and the set V(T 2n ) midpoint a n-1 The adjacent points of the dimension and the set V(T 2n-1 ) and the set V(T 2n ) to form an edge, and add the edge to store the 2n-1th independent spanning tree T 2n-1 The edge set E(T 2n-1 ) and store the 2nth independent spanning tree T 2n The edge set E(T 2n ), the set V(T 2n-1 ) and the set V(T 2n ) midpoint a n-1 The adjacent points of dimension are added to the set V(T 2n-1 ) and the set V(T 2n ), in the second layer, find the set V(T 2n-1 ) and the set V(T 2n ) n-2 dimensional adjacent points, and the set V(T 2n-1 ) and the set V(T 2n ) n-2 dimensional adjacent points and set V(T 2n-1 ) and the set V(T 2n ) to form an edge, and add the edge to the set E(T 2n-1 ) and the set E(T 2n ), the second layer set V(T 2n-1 ) and the set V(T 2n ) n-2 The adjacent points are added to the set V(T 2n-1 ) and the set V(T 2n ), and then build up to the nth layer, and find the set V(T 2n-1 ) and the set V(T 2n ) in the a0-dimensional adjacent points, the n-th layer set V(T 2n-1 ) and the set V(T 2n) and the set V(T 2n-1 ) and the set V(T 2n ) to form an edge, and add the edge to the set E(T 2n-1 ) and the set E(T 2n ), the n-th layer set V(T 2n-1 ) and the set V(T 2n ) in the a0-dimensional adjacent points are added to the set V(T 2n-1 ) and the set V(T 2n ), at this time, the 2n-1th independent spanning tree T 2n-1 and the 2nth independent spanning tree T 2n Complete the build.

[0036] A further improvement of the present invention is that step 5 is specifically as follows: different groups of independent spanning trees are obtained according to different circle arrangements, each group of independent spanning trees generates a group of non-intersecting paths, the average length of the path is calculated using the Dijkstra algorithm, a group of non-intersecting paths with the smallest average length is found, and data transmission is performed.

[0037] The beneficial effect of the present invention is that the present invention proposes an efficient parallel construction method. When a processor is designated as the source processor, that is, the root node of the spanning tree, a group of vertex independent spanning trees can be constructed in parallel with the processor as the center, thereby ensuring that there are 2n vertex-non-intersecting paths between the source processor and any other processors in the network.

[0038] In addition, the present invention can dynamically optimize and select a set of optimal non-intersecting paths according to different circle arrangement strategies. Based on this, data can be efficiently decomposed into these 2n paths for parallel transmission, and the paths do not interfere with each other, which significantly improves the efficiency and reliability of data transmission.

[0039] The core advantages of the present invention are: for any given vertex, 2n vertex independent spanning trees can be constructed in parallel; it is ensured that there are 2n point-disjoint paths between the root node and any other node; and each spanning tree can be constructed independently, with high flexibility and scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the parallel transmission method of the present invention.

[0041] Figure 2 It is a schematic diagram of the construction of the first independent spanning tree of the 3-ary n-cube structure of the present invention.

[0042] Figure 3 It is a schematic diagram of the construction of the second independent spanning tree of the 3-ary n-cube structure of the present invention.

[0043] Figure 4It is a schematic diagram of the construction of the 2i-1th independent spanning tree of the 3-ary n-cube structure of the present invention.

[0044] Figure 5 It is a schematic diagram of the construction of the 2ith independent spanning tree of the 3-ary n-cube structure of the present invention.

[0045] Figure 6 It is a schematic diagram of the construction of the 2n-1th independent spanning tree of the 3-ary n-cube structure of the present invention.

[0046] Figure 7 It is a schematic diagram of the construction of the 2nth independent spanning tree of the 3-ary n-cube structure of the present invention.

[0047] Figure 8 A schematic diagram of the structure of a group of non-intersecting paths constructed by the circular arrangement 021 of the present invention.

[0048] Fig. 9 It is a schematic diagram of the structure of a set of non-intersecting paths constructed by the circular arrangement 012 of the present invention.

[0049] Fig.10 The average failure transmission rate of the disjoint paths generated by the present invention when n=3, 4, 5.

[0050] Fig.11 It is the average failure transmission rate of the disjoint paths generated by the present invention when n is 6, 7, and 8.

[0051] Fig.12 When n=3, 4, 5, 6, the present invention is based on the average path length of the generated non-intersecting paths.

[0052] Fig.13 It is the average path length of the non-intersecting paths generated by the present invention when n is 6, 7, 8, and 9. DETAILED DESCRIPTION

[0053] The specific implementation of the present invention will be described in detail below in conjunction with the accompanying drawings. For ease of understanding, several specific implementation details will be described simultaneously in this specification. It should be particularly noted that these implementation details are only provided to better explain the present invention, and do not constitute any limitation on the scope of the present invention. Specifically, in certain implementations of the present invention, these detailed descriptions are not essential constituent elements.

[0054] The present invention provides a parallel data transmission method on a 3-element n-cube structure interconnection network, which constructs a cube structure according to given vertices. On (n-1)! A combination of 2n independent spanning trees with this vertex as the root; for For any Any vertex v is represented by an n-bit triple, such as v = vn-1 v n-2 …v0 makes N ± (v,i) represents the two adjacent points of v in dimension i, which are N + (v,i)=v n-1 v n-2 …(v i +1)mod3…v0,N - (v,i)=v n-1 v n-2 …(v i -1)mod3…v0; The 2n adjacent points of v are expressed as follows:

[0055] N + (v,0),N - (v,0),N + (v,1),N - (v,1),…,N + (v,n-1),N - (v,n-1).

[0056] like Figure 1 As shown, the present invention provides a method for parallel transmission of data on a 3-element n-cube structure interconnection network. The construction method is specifically as follows: firstly, a source processor is selected as the root node of the spanning tree, and a parallel construction is constructed with this as the center. The topology of multiple sets of independent spanning trees on the network is constructed. This structure can ensure that there are 2n non-intersecting communication paths between the source processor and any other processor in the network. By constructing multiple sets of independent spanning trees, multiple sets of non-intersecting paths can be obtained, and then the optimal path combination with the smallest average path length can be screened out. Based on this optimized path set, the system can decompose the data to be transmitted and distribute it in parallel to 2n non-interfering paths, thereby achieving efficient and reliable data transmission.

[0057] like Figure 1 As shown, the data parallel transmission method includes the following steps:

[0058] Step 1: Set the source node x=x n x n-1 …x1 is fixed as the root node of the independent spanning tree. According to the dimension n of the 3-tuple n-cube, find (n-1)! The circular permutation CDP is represented by an n-bit triple, that is, CDP = a n-1 a n-2 …a0;

[0059] The data center network of the present invention is a 3-dimensional n-cube structure. Based on, expressed as There is a direct edge between two nodes if and only if their identifiers differ by ±1 in one and only one dimension, modulo 3. n nodes, each node has a degree of 2n, that is, each node is directly connected to 2n adjacent nodes. The vertex number in this embodiment is represented by an n-bit triplet.

[0060] Step 2: Build the first independent spanning tree and the second independent spanning tree: Find the a of the source node x n-1 The two-dimensional adjacent points of are used as the first independent spanning tree and the second independent spanning tree with the source node x as the only child node of the root node, and then the following nodes are gradually established according to the circle arrangement CDP;

[0061] like Figure 2 and Figure 3 shown The first and second independent spanning trees are constructed by selecting the circle arrangement of 021. The present invention takes 000 as the root and first finds the 0-dimensional adjacent points 001 and 002 of 000. 001 is the only child node of the root node of the first independent spanning tree T1. At this time, the set V(T1) = {001}. 002 is the only child node of the root node of the second independent spanning tree T2. At this time, the set V(T2) = {002}. Then, find the 2-dimensional adjacent points of all points in V(T1). The two 2-dimensional adjacent points of 001 are 101 and 201. Connect points 101 and 201 to point 101. At this time, V(T1) = {001, 101, 201}. N + (002,2)=102,N - (002,2)=202, connect points 102 and 202 to 002. At this time, the set V(T2) is updated to {002, 102, 202}. Then find the 1-dimensional adjacent points of all points in the set V(T1), N + (001,1)=011,N - (001,2)=021,N + (101,1)=111,N - (101,1)=121,N + (201,1)=211,N -(201,1)=221, then connect the points in V(T1) with their adjacent points, that is, connect point 011 with point 021 and point 001, connect 111 and 121 with 101, and connect 221 with point 201. At this time, V(T1)={001, 101, 201, 011, 021, 111, 121, 211, 221}. Find the 1-dimensional adjacent points of all points in the set V(T2), similar to V(T1), and then connect the points in V(T2) with their adjacent points. At this time, V(T2)={002, 102, 202, 012, 022, 112, 122, 212, 222}. Finally, find the 0-dimensional adjacent points of all points in V(T1), N + (001,0)=002,N - (001,0)=000,N + (101,0)=102,N - (101,0)=100,N + (201,0)=202,N - (201,0)=200,N + (011,0)=012,N - (011,0)=010,N + (021,0)=022,N - (021,0)=020,N + (111,0)=112,N - (111,0)=110,N + (121,0)=122,N - (121,0)=120,N + (211,0)=212,N - (211,0)=210,N + (221,0)=222,N - (221,0)=220. Then connect the points in V(T1) to their adjacent points. Connect 002 and 000 to 001, connect 102 to 100 and 101, connect 202 to 200 and 201, connect 012 to 010 and 011, connect 022 to 020 and 021, connect 112, 110 to 111, connect 122 to 120 and 121, connect 212 to 210 and 211, and connect 222 to 220 and 221. At this time, Figure 2 As shown in T1, T1 is established. The steps of T2 are the same as T1. Find the 0-dimensional adjacent points of all points in V(T2) = {002, 102, 202, 012, 022, 112, 122, 212, 222}, and then connect the adjacent points with the points in the set, as shown in Figure 3The points created with the same color are created on the same layer.

[0062] Step 3: Establish the 2i-1th independent spanning tree and the 2ith independent spanning tree, 1<i<n-1, and select a of the source node x n-i The two dimensional adjacent points of the dimension are taken as the only child nodes of the root of the 2i-1th independent spanning tree and the 2ith independent spanning tree, and the subsequent nodes are gradually established according to the given circle arrangement CDP.

[0063] like Figure 4 and Figure 5 shown The construction of the 2i-1th and 2ith independent spanning trees. CDP = a n-1 a n-2 …a0=a2a1a0=021, at this time i is 2. First find the a of the root node 000 n-i dimensional adjacent point, i.e. a 3-2 = 2D adjacent points. The 2D adjacent points of 000 are N + (000,2)=100,N - (001,2)=200. Take point 100 as the only child node of the root node of the third tree T2, and take point 200 as the only child node of the root node of the fourth tree T3. At this time, the set V(T2)={100}, V(T3)={200}. Then, find the a of the midpoint of the set V(T2) and the set V(T3). (n-i-1)mod n = a0 = 1-dimensional adjacent points. The 1-dimensional adjacent points of 100 are 110 and 120 respectively. Connect 110 and 120 to 100. The 1-dimensional adjacent points of 200 are 210 and 220 respectively. Connect 210 to 220 and 200. At this time, V(T2) = {100, 110, 120}, V(T3) = {200, 210, 220}. Next, establish the second-level nodes of T2 and T3. Find the a of the sets V(T2) and V(T3) (n-i-2)mod n =a2=0-dimensional adjacent point. In set V(T2), the 0-dimensional adjacent points of 100 are 101 and 102, the 0-dimensional adjacent points of 110 are 111 and 112, and the 0-dimensional adjacent points of 120 are 121 and 122. Connect 111 and 112 to 110, connect 121 and 122 to 120, and connect points 101, 102 and 100. At this time, V(T2)={100, 110, 120, 101, 102, 111, 112, 121, 122}. In V(T3), construct the second layer of nodes in the same way and update V(T3)={200, 210, 220, 201, 202, 211, 212, 221, 222}. In the next layer, find a2 of sets V(T2) and V(T3). (n-i-n)mod n= a1 = 2D adjacent points. The 2D adjacent points of 100 are 200 and 000. Connect 200 and 000 to 100. The 2D adjacent points of 110 are 210 and 010, the 2D adjacent points of 120 are 020 and 220, the 2D adjacent points of 101 are 201 and 001, the adjacent points of 102 are 202 and 002, the 2D adjacent points of 111 are 011 and 211, the 2D adjacent points of 112 are 012 and 212, the 2D adjacent points of 121 are 021 and 221, and the 2D adjacent points of 122 are 022 and 222. Connect them separately, such as Figure 3 The yellow point in T2 is connected to the green point, thus T2 is constructed. Similarly, T3 is also constructed.

[0064] Step 4: Establish the 2n-1th independent spanning tree and the 2nth independent spanning tree, i.e. the last two independent spanning trees, find the adjacent points of the source node x in dimension a0, and then gradually establish the nodes of the spanning tree except the critical points of the source node x in dimension a0 according to the given circle arrangement.

[0065] like Figure 6 and Figure 7 shown The construction of the 2n-1th and 2nth independent spanning trees. In this case, n is 3. CDP = a n- 1a n-2 …a0=a2a1a0=021, first find the a0-dimensional neighboring point of the root node 000, that is, the 1-dimensional neighboring point. The 1-dimensional neighbors of 000 are 010 and 020. 010 is the only child node of the root node on T4, and 020 is the only child node of the root node on T3. At this time, V(T4)={010}, V(T5)={020}. Then, establish the first layer of nodes. Find the a0-th node in the sets V(T4) and V(T5). n-1 That is, 0-dimensional adjacent points, connect the adjacent points to the nodes in the original set. At this time, update the two sets, V(T4) = {010, 011, 012}, V(T5) = {020, 021, 022}. Then, establish the second layer of nodes of the independent spanning tree. Find the ath node in the sets V(T4) and V(T5). n-2 That is, 2D adjacent points. Connect the adjacent points to the nodes in the original set. At this time, update the two sets. After the update, V(T4) = {010, 011, 012, 210, 110, 111, 211, 112, 212}. At the same time, in the set V(T5), the points increase to {020, 021, 022, 220, 120, 121, 221, 122, 222}. Finally, establish the last layer of nodes. Find the 0D adjacent points in the sets V(T4) and V(T5), and connect the adjacent points to the nodes in the original set. The specific process is as follows: Figure 6 T4 and Figure 7 T5 is shown below.

[0066] Step 5: According to different arrangements of circles, find a set of optimal non-intersecting paths for parallel data transmission.

[0067] like Figure 8 and Fig. 9 The two different circular arrangements shown generate corresponding two groups of independent spanning trees. Taking the non-intersecting paths generated from point 000 to point 212 as an example, the total path length of a group of non-intersecting paths generated by circular arrangement 021 is 20, and the total path length of a group of non-intersecting paths generated by circular arrangement 012 is 21. Therefore, the present invention selects the first group of non-intersecting paths for secure data transmission.

[0068] The present invention can construct 2n point-independent spanning trees in parallel for any given vertex, and each tree can be constructed independently; at the same time, it ensures that there are 2n point-disjoint paths between the root node and any other node in the network. Thanks to its superior topological properties, the present invention can significantly reduce hardware costs and communication overheads, while optimizing the balance of communication costs. Therefore, the present invention shows great market potential in the wide application of interconnected network structures, and provides an efficient and reliable solution for high-performance computing and large-scale parallel systems.

[0069] The above embodiments are only used to illustrate the technical solutions of the present invention, and do not constitute any limitation on the protection scope of the present invention. Those skilled in the art should understand that any modification, equivalent replacement or improvement made to the technical solutions of the present invention, without departing from the design principle and spirit of the present invention, shall fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for parallel transmission of data on an interconnection network based on a 3-tuple n-cube, characterized in that: In a multiprocessor system based on a 3-dimensional n-cube interconnection network, a source node is a sender of data, a destination node is a receiver of data, and the edge between the source node and the destination node is a physical link or a virtual link to realize data transmission. Data is transmitted on the 3-dimensional n-cube interconnection network. The dimension of the 3-dimensional n-cube structure is n, and the connectivity is 2n. Suppose the source node is x=x n x n-1 x1, construct 2n independent spanning trees based on the source node and using it as the root, and the construction method of 2n independent spanning trees with a height of n+1, that is, the data parallel transmission method, includes the following steps: Step 1: Set the source node x=x n x n-1 …x1 is fixed as the root node of the independent spanning tree. According to the dimension n of the 3-tuple n-cube, find (n-1)! The circular permutation CDP is represented by an n-bit triple, that is, CDP = a n-1 a n-2 …a0; Step 2: Build the first independent spanning tree and the second independent spanning tree: Find the a of the source node x n-1 The two-dimensional adjacent points of are used as the first independent spanning tree and the second independent spanning tree with the source node x as the only child node of the root node, and then the following nodes are gradually established according to the circle arrangement CDP; Step 3: Establish the 2i-1th independent spanning tree and the 2ith independent spanning tree, 1<i<n-1, specifically: select a of the source node x n-i The two dimensional adjacent points of the dimension are used as the only child nodes of the root of the 2i-1th independent spanning tree and the 2ith independent spanning tree, and the subsequent nodes are gradually established according to the given circle arrangement CDP; Step 4: Establish the 2n-1th independent spanning tree and the 2nth independent spanning tree, i.e., the last two independent spanning trees, find the adjacent points of the source node x in dimension a0, and then gradually establish the nodes of the spanning tree except the critical points of the source node x in dimension a0 according to the given circle arrangement; Step 5: According to different arrangements of circles, find a set of optimal non-intersecting paths for parallel data transmission.

2. The method for parallel transmission of data on a 3-dimensional n-cube interconnection network according to claim 1, characterized in that: In step 1, according to the dimension n of the 3-dimensional n-cube, find (n-1)! The circular arrangement CDP=a n-1 a n-2 …a1 specifically includes the following steps: Step 1.1, determine the element set: generate a set S = {0, 1, 2, ..., n-1} containing n elements; Step 1.2: Generate a linear permutation without considering cyclic permutations. For n elements, the total number of linear permutations is the factorial of n. Step 1.3: For each linear permutation, fix one element and then generate all possible permutations. For each linear permutation, after fixing one element, the remaining elements generate a circular permutation. The total number of circular permutations is (n-1)! 3. The method for parallel transmission of data on a 3-dimensional n-cube interconnection network according to claim 1, characterized in that: The step 2 specifically includes the following steps: Step 2.1, build the first independent spanning tree T1 and the second independent spanning tree T2, find the source node x's a n-1 Two adjacent points of dimension: Among them, N + (x,a n-1 ) and N + (x,a n-1 ) are the only child nodes of the root nodes of the first independent spanning tree and the second independent spanning tree respectively; Step 2.2, put the only child node of the first independent spanning tree T1 in the set V(T1), and put the only child node of the second independent spanning tree T2 in the set V(T2), at this time V(T1) = {y1}, V(T2) = {y2}; Step 2.3, establish the following nodes layer by layer: in the first layer, find the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2), connect the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) with the points in the sets V(T1) and V(T2) to form edges, add the edges to the sets E(T1) and E(T2) storing the edges of the first independent spanning tree T1 and the second independent spanning tree T2, add the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) to the sets V(T1) and V(T2). V(T2); in the second layer, find the a1-dimensional adjacent points in the sets V(T1) and V(T2), connect the a1-dimensional adjacent points of the points in the sets V(T1) and V(T2) with the a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) to form edges, add the edges to the sets E(T1) and E(T2), and add the a1-dimensional adjacent points in the sets V(T1) and V(T2) in the second layer to the sets V(T1) and V(T2); in the nth layer, find the a1-dimensional adjacent points in the sets V(T1) and V(T2) n-1 dimensional adjacent points, and the n-th layer set V(T1) and the set V(T2) in a n-1 The a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) are connected to form edges, and the edges are added to the sets E(T1) and E(T2). The a0-dimensional adjacent points of the points in the sets V(T1) and V(T2) are added to the sets V(T1) and V(T2). At this time, the first independent spanning tree T1 and the second independent spanning tree T2 are established.

4. The method for parallel transmission of data on a 3-dimensional n-cube interconnection network according to claim 1, characterized in that: The step 3 specifically includes the following steps: Step 3.1, build the 2i-1th independent spanning tree and the 2ith independent spanning tree, and find the root node x's a n-i Two adjacent points of dimension: Among them, N + (x,a n-i ) and N - (x,a n-i ) are the only child nodes of the root nodes of the 2i-1th independent spanning tree and the 2ith independent spanning tree respectively; according to the circle arrangement, the following nodes are established layer by layer; Step 3.2: The 2i-1th independent spanning tree T 2i-1 The only child node is placed in the 2i-1th independent spanning tree T 2i-1 The set of points V(T 2i-1 ), the 2ith independent spanning tree T 2i The only child node is placed in the 2ith independent spanning tree T 2i The set of points V(T 2i ), at this time V(T 2i-1 )={y 2i-1 },V(T 2i )={y 2i }; Step 3.3, build the following nodes layer by layer: In the first layer, find the set V(T 2i-1 ) and the set V(T 2i ) midpoint a (n-i-1)modn dimensional adjacent points, the set V(T 2i-1 ) and the set V(T 2i ) midpoint a (n-i-1)modn The adjacent points of the dimension and the set V(T 2i-1 ) and the set V(T 2i ) to form an edge, and add the edge to store the 2i-1th independent spanning tree T 2i-1 The edge set E(T 2i-1 ) and store the 2ith independent spanning tree T 2i The edge set E(T 2i ), the set V(T 2i-1 ) and the set V(T 2i ) midpoint a (n-i-1)modn The adjacent points of dimension are added to the set V(T 2i-1 ) and the set V(T 2i ), in the second layer, find the set V(T 2i-1 ) and the set V(T 2i ) (n-i-2)modn dimensional adjacent points, will be set in the second layer V(T 2i-1 ) and the set V(T 2i ) (n-i-2)modn dimensional adjacent points and set V(T 2i-1 ) and the set V(T 2i ) to form an edge, and add the edge to the set E(T 2i-1 ) and the set E(T 2i ), the set V(T 2i-1 ) and the set V(T 2i ) (n-i-2)modn The adjacent points are added to the set V(T 2i-1 ) and the set V(T 2i ), in the next layer, find the set V(T 2i-1 ) and the set V(T 2i ) (n-i-3)modn The adjacent points are thus established until the nth layer, and the set V(T 2i-1 ) and the set V(T 2i ) n-i dimensional adjacent points, the n-th layer set V(T 2i-1 ) and the set V(T 2i ) n-i dimensional adjacent points and the set E(T 2i-1 ) and the set E(T 2i ) to form an edge, and add the edge to the set E(T 2i-1 ) and the set E(T 2i ), the n-th layer set V(T 2i-1 ) and the set V(T 2i ) n-i The adjacent points are added to the set V(T 2i-1 ) and the set V(T 2i ), at this time, the 2i-1th independent spanning tree T 2i-1 and the 2ith independent spanning tree T 2i Complete the build.

5. The method for parallel transmission of data on a 3-dimensional n-cube interconnection network according to claim 1, characterized in that: The step 4 specifically includes the following steps: Step 4.

1. Establish the 2n-1th independent spanning tree and the 2nth independent spanning tree, and find the two adjacent points of the root node x in dimension a0: Among them, N + (x,a0) is the only child node of the 2n-1th independent spanning tree, N - (x,a0) is the only child node of the 2nth independent spanning tree; Step 4.2: The 2n-1th independent spanning tree T 2n-1 The only child node is placed in the set V(T 2n-1 ), the 2nth independent spanning tree T 2n The only child node is placed in the set V(T 2n ), at this time V(T 2n-1 )={y 2n-1 },V(T 2n )={y 2n }; Step 4.3, build the following nodes layer by layer: In the first layer, find the set V(T 2n-1 ) and the set V(T 2n ) midpoint a n-1 dimensional adjacent points, the set V(T 2n-1 ) and the set V(T 2n ) midpoint a n-1 The adjacent points of the dimension and the set V(T 2n-1 ) and the set V(T 2n ) to form an edge, and add the edge to store the 2n-1th independent spanning tree T 2n-1 The edge set E(T 2n-1 ) and store the 2nth independent spanning tree T 2n The edge set E(T 2n ), the set V(T 2n-1 ) and the set V(T 2n ) midpoint a n-1 The adjacent points of dimension are added to the set V(T 2n-1 ) and the set V(T 2n ), in the second layer, find the set V(T 2n-1 ) and the set V(T 2n ) n-2 dimensional adjacent points, and the set V(T 2n-1 ) and the set V(T 2n ) n-2 dimensional adjacent points and set V(T 2n-1 ) and the set V(T 2n ) to form an edge, and add the edge to the set E(T 2n-1 ) and the set E(T 2n ), the second layer set V(T 2n-1 ) and the set V(T 2n ) n-2 The adjacent points are added to the set V(T 2n-1 ) and the set V(T 2n ), and then build up to the nth layer, and find the set V(T 2n-1 ) and the set V(T 2n ) in the a0-dimensional adjacent points, the n-th layer set V(T 2n-1 ) and the set V(T 2n ) and the set V(T 2n-1 ) and the set V(T 2n ) to form an edge, and add the edge to the set E(T 2n-1 ) and the set E(T 2n ), the n-th layer set V(T 2n-1 ) and the set V(T 2n ) in the a0-dimensional adjacent points are added to the set V(T 2n-1 ) and the set V(T 2n ), at this time, the 2n-1th independent spanning tree T 2n-1 and the 2nth independent spanning tree T 2n Complete the build.

6. The method for parallel transmission of data on a 3-dimensional n-cube interconnection network according to claim 1, characterized in that: The step 5 is specifically as follows: different groups of independent spanning trees are obtained according to different circle arrangements, each group of independent spanning trees generates a group of non-intersecting paths, the average length of the paths is calculated using the Dijkstra algorithm, a group of non-intersecting paths with the smallest average length is found, and data transmission is performed.

Images