Method for parallel transmission of data on a 3-ary n-cube based interconnection network

Abstract

The application belongs to the technical field of communication, and discloses a parallel transmission method of data on an interconnection network based on a 3-m n-cube. According to the dimension n of the 3-m n-cube, (n-1)! groups of circular arrangements are found, and then according to each group of circular arrangements, an independent spanning tree is gradually established by a node x. Different circular arrangements generate independent spanning trees of different groups. The independent spanning trees of different groups correspond to different groups of disjoint paths. According to different circular arrangements, a group of optimal disjoint paths is found, and parallel data transmission is performed. The application can significantly reduce communication overhead, optimize the balance of communication cost, and has great market potential in the wide application of interconnection network structures, and provides an efficient and reliable solution for high-performance computing and large-scale parallel systems.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of communication, and specifically relates to a parallel transmission method of data on a 3-ary n-cube structure interconnected network. BACKGROUND

[0002] The rapid development of artificial intelligence technology has posed unprecedented demands on high performance computing (HPC), driving the continuous growth of computing resources. As a core research tool for realizing major scientific breakthroughs, HPC mainly relies on parallel and distributed systems, and the design and performance of the interconnection network play a decisive role. The interconnection network is usually described in a graph theory model, in which processors are abstracted as vertices and communication links between processors are represented as edges. In this context, hypercube, as a classic interconnection network topology, is 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 node degree also increases. This increase in node degree can bring additional complexity to parallel computing systems, such as higher hardware costs and communication overhead, thus becoming a potential challenge in system design.

[0003] 3-ary n-cube, As an important extension of hypercube, 3-ary n-cube is an excellent interconnection network topology. It inherits the core advantages of hypercube such as low latency, high symmetry, and scalability, while further introducing new features such as reducing message transmission delay and simplifying hardware implementation, making it exhibit significant application value in the field of parallel computing and supercomputers. With the continuous deepening of interconnection network research, its construction strategy also shows broad prospects in data center networks, providing new solutions to improve the efficiency and reliability of large-scale data processing.

[0004] In an interconnection network based on a 3-ary n-cube topology network, as the scale of the processor expands, 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-scale data to the target processor, these point disjoint links can be achieved by vertex independent spanning trees (IST). Specifically, for a given network, vertex independent spanning trees refer 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 vertex except the root node in all spanning trees. However, the existing construction method of point independent spanning trees in 3-ary n-cube network mainly relies on a serial recursive algorithm, which has high time complexity and is difficult to meet the efficient needs of large-scale networks. SUMMARY

[0005] To solve the above technical problems, the present application provides a parallel data transmission method on a 3-ary n-cube structure interconnection network, which can construct 2n point independent spanning trees in parallel for any given vertex, and each tree can be constructed independently, while ensuring that there are 2n point disjoint paths between the root node and any other node in the network.

[0006] To achieve the above purpose, the present application is realized by the following technical scheme:

[0007] The present application is a parallel data transmission method based on a 3-ary n-cube interconnection network, which is based on a 3-ary n-cube structure interconnection network. In a multi-processor system based on a 3-ary n-cube structure interconnection network, the source node is the sender of the data, the destination node is the receiver of the data, the edge between the source node and the destination node is the physical link or virtual link to realize data transmission, and the point-point independent spanning tree can be constructed with the source node as the root node to obtain multiple disjoint paths, thereby reducing transmission time, reducing communication delay, enhancing fault tolerance of data transmission, etc. Data is transmitted on a 3-ary n-cube structure interconnection network. The 3-ary n-cube structure has a dimension of n and a connectivity of The source node is , and n independent spanning trees are constructed according to the source node and taking it as the root node. Any vertex is represented by an n-bit ternary group: To better represent the relationship between points, the present application uses table point Two adjacent points of the point are , ; each height is The method for constructing 2n independent spanning trees, i.e., the data parallel transmission method, comprises the following steps:

[0008] Step 1: Set the source node Fixed as the root node of the independent spanning tree, according to the dimension n of the 3-ary n-cube, find The circular permutation CDP is represented by n-bit triples, that is, ;

[0009] Step 2: Establish the first independent spanning tree and the second independent spanning tree: Find the source node of The two-dimensional adjacent points of , take these two-dimensional adjacent points as the first independent spanning tree and the second independent spanning tree with the source node It is 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: Create the Independent spanning tree and Independent spanning trees, , specifically: Select the source node of The two adjacent points of the dimension are taken as the first Independent spanning tree and The only child node of the root of an independent spanning tree, which gradually establishes subsequent nodes according to the given circle arrangement CDP;

[0011] Step 4: Create the Independent spanning trees and The last two independent spanning trees are independent spanning trees, and the source node is found. of dimensional adjacent points, and then gradually build the spanning tree according to the given circle arrangement except the source node of Nodes outside the critical point of the dimension;

[0012] Step 5: Based on different circle arrangements, find a set of optimal non-intersecting paths for parallel data transmission.

[0013] A further improvement of the present invention is that in step 1, according to the dimension n of the 3-element n-cube, find Circle arrangement The specific steps include:

[0014] Step 1.1, determine the element set: generate a A collection of elements ;

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

[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 .

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

[0018] Step 2.1: Create the first independent spanning tree and the second independent spanning tree , find the source node of Two adjacent points of dimension:

[0019]

[0020]

[0021] in, and The only child node of the root node of the first independent spanning tree and the second independent spanning tree respectively;

[0022] Step 2.2: The first independent spanning tree The only child node is placed in the collection In the second independent spanning tree The only child node is placed in the collection In, at this time , ;

[0023] Step 2.3, build the following nodes layer by layer: In the first layer, find the set and collection midpoint dimensional adjacent points, the set of and collection midpoint Dimensional adjacencies and sets and collection The points in the form of edges are connected, and the edges are added to store the first independent spanning tree. The set of edges and the second independent spanning tree The set of edges , will be collected and collection midpoint The adjacent points of the dimension are added into the set and the set In the second layer, find the adjacent points of the dimension in the set and the set In the set The adjacent points of the dimension are added into the set and the set In the set The adjacent points of the dimension are added into the set and the set In the set The points in the adjacent points of the dimension are connected to form edges, and the edges are added into the set and the set In the second layer, find the adjacent points of the dimension in the set and the set In the set The adjacent points of the dimension are added into the set and the set In the n-th layer, find the adjacent points of the dimension in the set and the set In the set The adjacent points of the dimension are added into the set and the set In the set The points in the adjacent points of the dimension are connected to form edges, and the edges are added into the set and the set In the set The adjacent points of the dimension are added into the set and In the set The points in the adjacent points of the dimension are connected to form edges, and the edges are added into the set and the set In the set The adjacent points of the dimension are added into the set In the set The first independent spanning tree and the second independent spanning tree are completed.

[0024] The further improvement of the application is that step 3 specifically comprises the following steps:

[0025] Step 3.1, establishing the first independent spanning tree and the second independent spanning tree, finding two adjacent points of the dimension of the root node:

[0026]

[0027]

[0028] wherein, and are the first​​​​​ an independent spanning tree and the root node of an independent spanning tree; according to the circular arrangement, the following nodes are established layer by layer;

[0029] Step 3.2, the unique child node of the independent spanning tree is placed in the point set of the independent spanning tree ; the unique child node of the independent spanning tree is placed in the point set of the independent spanning tree ; at this time , ;

[0030] Step 3.3, the following nodes are established layer by layer: in the first layer, the adjacent points of the dimension of the points in the set and the set are found, the adjacent points of the dimension of the points in the set and the set are connected to the points in the set and the set , forming edges, the edges are added to the set storing the edges of the independent spanning tree and the set storing the edges of the independent spanning tree , the adjacent points of the dimension of the points in the set and the set are added to the set and the set , in the second layer, the dimension adjacent points in the set and the set are found, the dimension adjacent points in the set and the set in the second layer are connected to the points in the set and the set , forming edges, the edges are added to the set and the set , the dimension adjacent points in the set and the set in the second layer are added to the set and the set In the next layer, find the set and the set in which the adjacent point of dimension n is located, and the set of the adjacent point of dimension n in the nth layer is found and the set in which the adjacent point of dimension n is located, and the adjacent point of dimension n in the set is connected to the set and the set in which the point is located, forming an edge, and the edge is added to the set and the set , and the adjacent point of dimension n in the nth layer set and the set in which the adjacent point of dimension n is located is added to the set and the set , and at this time the independent spanning tree and the independent spanning tree is completed.

[0031] The further improvement of the present application is that step 4 specifically comprises the following steps:

[0032] Step 4.1, establishing the independent spanning tree and the independent spanning tree, finding two adjacent points of dimension of the root node :

[0033]

[0034]

[0035] wherein, is the only child node of the independent spanning tree, the only child node of the independent spanning tree;

[0036] Step 4.2, placing the only child node of the independent spanning tree in the set , and placing the only child node of the independent spanning tree in the set , at this time , ;

[0037] Step 4.3, layer by layer, the following nodes are established: in the first layer, find the set and set of midpoints of dimensional neighbors of the points in set and set of midpoints of dimensional neighbors of the points in set and set of edges connecting the points in set to set of edges of the first independent spanning tree and set of edges of the second independent spanning tree , set of edges of the first independent spanning tree and set of midpoints of dimensional neighbors of the points in set and set of midpoints of dimensional neighbors of the points in set and set of edges connecting the points in set to set of edges connecting the points in set to set and set of edges connecting the points in set to set of edges of the first independent spanning tree and set of midpoints of dimensional neighbors of the points in set and set of midpoints of dimensional neighbors of the points in set and set of edges connecting the points in set to set of edges connecting the points in set to set and set of edges connecting the points in set to set of edges of the first independent spanning tree and set of midpoints of dimensional neighbors of the points in set and set of midpoints of dimensional neighbors of the points in set and set of edges of the second independent spanning tree are complete.

[0038] The further improvement of the present application is that step 5 is specifically: according to different circle arrangements, different groups of independent spanning trees are obtained, each group of independent spanning trees generates a group of disjoint paths, the average length of the paths is calculated by using the Dijkstra algorithm, the group of disjoint paths with the minimum average length is found out, and data transmission is performed.

[0039] The beneficial effects of the present application are: the present application proposes an efficient parallel construction method, when a certain processor is specified as a source processor, i.e., 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, so that there are 2n paths between the source processor and any other processor in the network.

[0040] In addition, the present application can dynamically optimize and select a group of optimal disjoint paths according to different circle arrangement strategies. Based on this, data can be efficiently decomposed into the 2n paths for parallel transmission, and the paths do not interfere with each other, which significantly improves the efficiency and reliability of data transmission.

[0041] The core advantage of the present application is that: 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 independently constructed, which has high flexibility and scalability. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a flowchart of the parallel transmission method of the present application.

[0043] Figure 2 is a construction schematic diagram of the first independent spanning tree of the 3-ary n-cube structure of the present application.

[0044] Figure 3 is a construction schematic diagram of the second independent spanning tree of the 3-ary n-cube structure of the present application.

[0045] Figure 4 is a construction schematic diagram of the third independent spanning tree of the 3-ary n-cube structure of the present application.

[0046] Figure 5 is a construction schematic diagram of the fourth independent spanning tree of the 3-ary n-cube structure of the present application.

[0047] Figure 6 is a construction schematic diagram of the fifth independent spanning tree of the 3-ary n-cube structure of the present application.

[0048] Figure 7 is a construction schematic diagram of the sixth independent spanning tree of the 3-ary n-cube structure of the present application. ​​​Schematic diagram of the construction of an independent spanning tree.

[0049] Figure 8 A schematic diagram of the structure of a set of non-intersecting paths constructed by circular arrangement 021 in the present invention.

[0050] Figure 9 It is a structural schematic diagram of a set of non-intersecting paths constructed by the circular arrangement 012 of the present invention.

[0051] Figure 10 It is the average failure transmission rate of the disjoint paths generated by the present invention when n is 3, 4, and 5.

[0052] Figure 11 It is the average failure transmission rate of the disjoint paths generated by the present invention when n is 6, 7, and 8.

[0053] Figure 12 It is the average path length of the non-intersecting paths generated by the present invention when n is 3, 4, 5, and 6.

[0054] Figure 13 It is the average path length of the non-intersecting paths generated by the present invention when n is 7, 8, 9, and 10. DETAILED DESCRIPTION

[0055] The following will describe in detail the specific embodiments of the present invention in conjunction with the accompanying drawings. For ease of understanding, several specific implementation details will be described in this specification. It should be noted that these implementation details are provided solely to better explain the present invention and do not constitute any limitation on the scope of the present invention. Specifically, in certain embodiments of the present invention, these detailed descriptions are not essential components.

[0056] 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. (n-1)! groups A combination of independent spanning trees with this vertex as the root; for , for any , any vertex All by Bit triples are represented as make express of The two adjacent points of dimension are , ; middle The 2n adjacent points of are expressed as follows:

[0057] .

[0058] likeFigure 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: first, a source processor is selected as the root node of the spanning tree, and a parallel construction is constructed with this as the center. Multiple groups of vertices on the network independently generate a tree topology. This structure ensures that there is a connection between the source processor and any other processor in the network. By constructing multiple independent spanning trees, we can obtain multiple sets of point-disjoint paths, and then filter out the optimal path combination with the smallest average path length. Based on this optimized path set, the system can decompose the data to be transmitted and distribute it in parallel to The two paths do not interfere with each other, thus achieving efficient and reliable data transmission.

[0059] like Figure 1 As shown, the data parallel transmission method includes the following steps:

[0060] Step 1: Set the source node Fixed to the root node of the independent spanning tree, according to the dimensions of the 3-ary n-cube ,turn up CDP with circular arrangement, CDP with circular arrangement The bit triplet represents ;

[0061] The data center network of the present invention is a 3-dimensional n-cube structure. Based on There is a direct edge between two nodes if and only if their identifiers differ by ±1 in one dimension only, modulo 3. 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.

[0062] Step 2: Establish the first independent spanning tree and the second independent spanning tree: Find the source node of The two-dimensional adjacent points of , take these two-dimensional adjacent points as the first independent spanning tree and the second independent spanning tree with the source node It is the only child node of the root node, and then the following nodes are gradually established according to the circle arrangement CDP;

[0063] like Figure 2 and Figure 3 shown The first and second independent spanning trees are constructed by selecting a 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 used as the first independent spanning tree. The unique child of the root node, at this time, the set .002 is the second independent spanning tree The unique child of the root node, at this time, the set Then, find The 2-dimensional adjacent points of all points in the set, the two 2-dimensional adjacent points of 001 are 101 and 201, connect points 101 and 201 to point 101, at this time, the set . , Connect point 102 and point 202 to 002, at this time, the set is updated to Again, find the 1-dimensional adjacent points of all points in the set , , , , , , Again, connect the points in the set to their adjacent points respectively, that is, connect points 011 and 021 to point 001, connect 111 and 121 to point 101, and connect 221 to point 201. At this time, the set . Find the 1-dimensional adjacent points of all points in the set , similar to , again connect the points in the set to their adjacent points respectively. At this time, the set . Finally, find the 0-dimensional adjacent points of all points in the set , , , , , , , , , , , , , , , , , , . Again, connect the points in the set to their adjacent points respectively. 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 and 120 to 121, connect 212 and 210 to 211, and connect 222 and 220 to 221. At this time, asFigure 2 of As shown, The build is complete. Steps and Same, find The 0-dimensional adjacent points of all points in , and then connect the adjacent points with the points in the set, such as Figure 3 of As shown in the figure, points created with the same color are created on the same layer.

[0064] Step 3: Create the Independent spanning tree and Independent spanning trees, , select the source node of The two adjacent points of the dimension are taken as the first Independent spanning tree and The only child node of the root of an independent spanning tree, which gradually establishes subsequent nodes according to the given circle arrangement CDP.

[0065] like Figure 4 and Figure 5 shown No. Kehedi The construction of independent spanning trees. , i is 2 at this time. First find the root node 000 dimensional adjacent points dimensional adjacent points. The 2-dimensional adjacent points of 000 are , . Take point 100 as the third tree The only child node of the root node, with point 200 as the fourth tree The only child node of the root node. , Then, find the set and collection midpoint 1-dimensional adjacent points. The 1-dimensional adjacent points of 100 are 110 and 120 respectively. Connect 110 and 120 with 100. The 1-dimensional adjacent points of 200 are 210 and 220 respectively. Connect 210 with 220 and 200. At this time, , . The following is established and The second layer of nodes. Find the set and of dimensional adjacent points. In the set In the example, 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. .exist Similarly, build the second layer of nodes and update In the next layer, find the set and of 2D adjacent points. 100's 2D adjacent points are 200 and 000. Connect 200 and 000 to 100. 110's 2D adjacent points are 210 and 010, 120's 2D adjacent points are 020 and 220, 101's 2D adjacent points are 201 and 001, 102's 2D adjacent points are 202 and 002, 111's 2D adjacent points are 011 and 211, 112's 2D adjacent points are 012 and 212, 121's 2D adjacent points are 021 and 221, and 122's 2D adjacent points are 022 and 222. Connect them separately, as shown in the following example: Figure 3 of The yellow point is connected to the green point, so The construction is completed. Similarly, Also built.

[0066] Step 4: Create the Independent spanning trees and The last two independent spanning trees are independent spanning trees, and the source node is found. of dimensional adjacent points, and then gradually build the spanning tree according to the given circle arrangement except the source node of Nodes outside the critical point of the dimension.

[0067] like Figure 6 and Figure 7 shown No. Kehedi In this case, n is 3. , first find the root node 000 The one-dimensional adjacent points are 1-dimensional adjacent points. The one-dimensional adjacent points of 000 are 010 and 020. 010 is The only child node of the root node, 020 is The only child node of the root node. , Then, build the first layer of nodes. Find the set and Middle Right now Dimension adjacent points, connect the adjacent points to the nodes in the original set. At this time, update the two sets, , Then, build the second layer of nodes of the independent spanning tree. Find the set and Middle Right now Dimensional adjacent points. Connect the adjacent points to the nodes in the original set. At this time, update the two sets. After the update, , at the same time, in the collection In the middle, the point increases to Finally, build the last layer of nodes. Find the set and middle Dimensional adjacent points, connect the adjacent points to the nodes in the original set. The specific process is as follows Figure 6 of and Figure 7 of shown.

[0068] Step 5: Based on different circle arrangements, find a set of optimal non-intersecting paths for parallel data transmission.

[0069] like Figure 8 and Figure 9 The two groups of independent spanning trees generated by the two different circular arrangements shown are taken as an example of the non-intersecting paths generated from point 000 to point 212. The total path length of the group of non-intersecting paths generated by the circular arrangement 021 is 20, and the total path length of the group of non-intersecting paths generated by the circular arrangement 012 is 21. Therefore, the present invention selects the first group of non-intersecting paths for secure data transmission.

[0070] The present invention can construct 2n independent spanning trees in parallel for any given vertex, with each tree being independently constructed. Simultaneously, 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 overhead while optimizing the balance of communication costs. Therefore, the present invention exhibits significant market potential in a wide range of interconnected network architectures, providing an efficient and reliable solution for high-performance computing and massively parallel systems.

[0071] The above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. It should be understood by those skilled in the art that any modification, equivalent replacement, or improvement of the technical solutions of the present invention, without departing from the design principles and spirit of the present invention, shall fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for parallel transmission of data on a 3-ary n-cube based interconnection network, characterized by: In a multiprocessor system based on a 3-dimensional n-cube structure interconnection network, a source node is a sender of data, a destination node is a receiver of data, an edge between the source node and the destination node is a physical link or a virtual link to realize data transmission, and data is transmitted on the 3-dimensional n-cube structure interconnection network, the dimension of the 3-dimensional n-cube structure is n, and the connectivity is , the source node is , and a plurality of independent spanning trees are constructed according to the source node and taking the source node as a root , the height of each of the independent spanning trees is A construction method of 2n independent spanning trees, i.e., a data parallel transmission method, comprises the following steps: Step 1, the source node is fixed as the root node of the independent spanning tree, according to the dimension n of the 3-ary n-cube, find CDP, the circular arrangement CDP is expressed by n-bit triplets, that is ; Step 2: Establish the first independent spanning tree and the second independent spanning tree: Find the source node of The two adjacent points of the dimension are used as the first independent spanning tree and the second independent spanning tree with the source node It is the only child node of the root node, and then the following nodes are gradually established according to the circle arrangement CDP; Step 3, establishing the first independent spanning tree and the second independent spanning tree, Specifically, selecting two dimension adjacent points of the source node dimension, taking the two dimension adjacent points as the only child nodes of the root of the first independent spanning tree and the second independent spanning tree, and gradually establishing subsequent nodes according to the given circle arrangement CDP.​ Step 4, establishing the first independent spanning tree and the second independent spanning tree, finding the adjacent point of the source node of the dimension, and then establishing the nodes except the adjacent point of the source node of the dimension according to the given circle arrangement step by step. Step 5, according to different circle arrangement, find out a set of optimal disjoint paths, carry out data parallel transmission, specifically: according to different circle arrangement, get different groups of independent spanning tree, each group of independent spanning tree generates a group of disjoint paths, calculates the average length of the path by using Dijkstra algorithm, finds out a group of disjoint paths with the minimum average length, and carries out data transmission.

2. The method for parallel transmission of data over a 3 -dimensional n-cube based interconnection network as claimed in claim 1, wherein: In the step 1, according to the dimension n of the 3 -dimensional n-cube, find Group circle arrangement Specifically comprises the following steps: Step 1.

1. Determine the set of elements: generate a set containing one element ; Step 1.

2. Generate a linear permutation that does not consider the cyclic permutation, for the total number of linear permutations is the factorial of the number of elements; Step 1.3, for each linear arrangement, fix one element, then generate all possible arrangements, for each linear arrangement, fix one element, then generate a circular arrangement of the remaining elements, the total number of circular arrangements is .

3. The method for parallel transmission of data over a 3 -dimensional n-cube based interconnection network as claimed in claim 1, wherein: The step 2 specifically includes the following steps: Step 2.1, Establishing the first independent spanning tree and the second independent spanning tree , finding the source node of two adjacent points of the dimension ， ， wherein, and are unique child nodes of the root node of the first and second independent spanning tree, respectively. Step 2.2, the first independent spanning tree puts its unique child in the set Step 2.3, the second independent spanning tree puts its unique child in the set Step 2.4, the third independent spanning tree , ; Step 2.3, build the following nodes layer by layer: In the first layer, find the set and collection midpoint dimensional adjacent points, the set of and collection midpoint Dimensional adjacencies and sets and collection The points in the form of edges are connected, and the edges are added to store the first independent spanning tree. The set of edges and the second independent spanning tree The set of edges , will be collected and collection midpoint The adjacent points of the dimension are added to the set and collection Inside; on the second floor, find the collection and collection in dimensional adjacent points, the set and collection midpoint Dimensional adjacencies and sets and collection midpoint The points in the adjacent points of the dimension are connected to form edges, and the edges are added to the set and collection , the second layer is collected and collection in Dimensional adjacent points join the set and collection In the nth layer, find the set and collection in dimensional adjacent points, the n-th layer set and collection in Dimensional adjacencies and sets and collection midpoint The points in the adjacent points of the dimension are connected to form edges, and the edges are added to the set and , will be collected and collection midpoint The adjacent points of the dimension are added to the set and collection At this time, the first independent spanning tree and the second independent spanning tree Complete the establishment.

4. The method for parallel transmission of data over a 3 -dimensional n-cube based interconnection network as claimed in claim 1, wherein: The step 3 specifically includes the following steps: Step 3.1, establish the first independent spanning tree and the second independent spanning tree, find the root node of the dimension of two adjacent points: ， ， wherein, and are the first independent spanning tree and the second independent spanning tree root node, respectively; according to the circle arrangement, the following nodes are established layer by layer; Step 3.2, the first independent spanning tree is placed in the set of points of the first independent spanning tree , the second independent spanning tree is placed in the set of points of the first independent spanning tree , the third independent spanning tree is placed in the set of points of the first independent spanning tree , and so on. Step 3.3, build the following nodes layer by layer: In the first layer, find the set and collection midpoint dimensional adjacent points, the set and collection midpoint Dimensional adjacencies and sets and collection The midpoints are connected to form a link, and the link is added to the storage Independent spanning trees The set of edges and store the Independent spanning trees The set of edges , will be collected and collection midpoint The adjacent points of the dimension are added to the set and collection Inside, on the second floor, find the collection and collection in dimensional adjacent points, which will be collected in the second layer and collection in Dimensional adjacencies and sets and collection Connect the points in the grid to form edges, and add the edges to the set and collection , the second layer is collected and collection in Dimensional adjacent points join the set and collection Inside, on the next level, find the collection and collection in The dimension adjacent points are thus established until the nth layer, and the set and collection in dimensional adjacent points, the n-th layer set and collection in Dimensional adjacencies and sets and collection The midpoints are connected to form edges, and the edges are added to the set and collection , the nth layer set and collection in Dimensional adjacent points join the set and collection Inside, at this time a spanning tree and the a spanning tree the establishment is completed.

5. The method for parallel transmission of data over a 3 -dimensional n-cube based interconnection network as claimed in claim 1, wherein: The step 4 specifically includes the following steps: Step 4.1, establish the first independent spanning tree and the second independent spanning tree, find the root node of the dimension of the two adjacent points: ， ， wherein, is the unique child of the is the unique child of the Step 4.2, put the first independent spanning tree unique child in the set of trees, put the first independent spanning tree unique child in the set of trees, and now , ; Step 4.3, build the following nodes layer by layer: In the first layer, find the set and collection midpoint dimensional adjacent points, the set and collection midpoint Dimensional adjacencies and sets and collection Connect the points in the Independent spanning trees The set of edges and store the Independent spanning trees The set of edges , collect the first layer and collection midpoint The adjacent points of the dimension are added to the set and collection Inside, on the second floor, find the collection and collection in dimensional adjacent points, the set and collection in Dimensional adjacencies and sets and collection Connect the points in the grid to form edges, and add the edges to the set and collection , the second layer is set and collection in Dimensional adjacent points join the set and collection In, from this, until the nth layer, find the set and collection in dimensional adjacent points, the n-th layer set and collection in Dimensional adjacencies and sets and collection Connect the points in the grid to form edges, and add the edges to the set and collection , the nth layer set and collection in Dimensional adjacent points join the set and collection Inside, at this time Independent spanning trees Hedi Independent spanning trees The establishment is completed.

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