Method and system for constructing multipath fault-tolerant communication based on torus graph

Abstract

This invention discloses a method and system for constructing multi-path fault-tolerant communication based on a Torus line graph, belonging to the field of fault-tolerant communication technology for interconnected networks. The method includes: obtaining the scale parameters of a two-dimensional Torus network, constructing the original Torus graph and mapping it to a Torus line graph; selecting a common root node and determining six root gateways among its six neighboring nodes; configuring the backbone region, backbone advancement direction, and root endpoint for each of the six independent vertex spanning trees; constructing representative states for any non-root line graph node, uniquely determining the parent node based on its region and incoming direction type, and generating six independent vertex spanning trees centered on the common root node; extracting six root paths, and making fault-tolerant communication decisions by determining whether internal nodes of the path intersect with the fault set under link failure conditions. This invention can uniformly construct six independent communication paths for internal nodes on the Torus line graph, significantly improving link-level fault-tolerant communication capabilities and system reliability.

Description

Technical Field

[0001] This invention relates to the field of interconnection network communication and fault tolerance technology, specifically to a method and system for constructing multi-path fault-tolerant communication based on Torus line graphs. Background Technology

[0002] With the continuous development of high-performance computing, cloud computing, and large-scale data center technologies, interconnected networks, as the infrastructure for data exchange and task collaboration between computing nodes, directly affect the system's communication latency, throughput, scalability, and fault tolerance performance through their topology. In parallel computing systems, distributed storage systems, and data center networks, how to construct a network topology that is both structurally sound and easily scalable, while maintaining high communication reliability under link failure conditions, has become a crucial and ongoing concern in this field.

[0003] In graph theory modeling, interconnected networks are typically abstracted as undirected graphs G=(V,E), where the vertex set V represents the set of communication nodes such as processors or servers, and the edge set E represents the set of physical links or logical connections between nodes. For a given network topology, if several spanning trees with a common root node can be constructed on it, these spanning trees can be used as a communication framework for broadcasting, aggregation, path recovery, or fault-tolerant transmission. A spanning tree is a connected subgraph in the network that covers all vertices and contains no cycles. If a set of spanning trees shares the same common root node r, and for any vertex v∈V other than r, the paths from vertex v to the common root node r in different spanning trees are pairwise disjoint except at the root node, then these spanning trees are called a set of vertex-independent spanning trees. Vertex-independent spanning trees can provide multiple independent communication paths between the same source (root) node and the same destination node, and have significant application value in scenarios such as fault-tolerant broadcasting, reliable communication, and secure distribution of information.

[0004] In existing technologies, considerable research has been conducted on multipath fault-tolerant communication for regular network topologies, such as hypercubes, chordal networks, and Torus networks. Among these, Torus networks are widely considered a typical network structure suitable for large-scale parallelism and data center interconnection due to their advantages such as regular structure, good symmetry, constant node degree of 4, uniform path distribution, and ease of expansion. Let a two-dimensional Torus network be denoted as... T(n,m)=C n ×C m , Among them, C n and C m Let represent loop graphs of length n and m respectively, and × denote the Cartesian product of the graphs. Therefore, the vertex set of a two-dimensional Torus network can be represented as... V(T(n,m))={(r,c)|0≤r≤n-1, 0≤c≤m-1} Where r represents the row coordinate and c represents the column coordinate. For any vertex (r, c), it is adjacent to (r, c+1 mod m) and (r, c-1 mod m) in the horizontal direction and to (r+1 mod n, c) and (r-1 mod n, c) in the vertical direction. Therefore, T(n, m) is a 4-regular undirected graph.

[0005] To more precisely characterize the relationships between links in a network, existing graph theory research often introduces the concept of a line graph. Let G=(V,E) be an undirected graph, and its line graph be denoted as L(G). In the line graph L(G), each edge e∈E in the original graph G corresponds to a vertex in the line graph; if two edges in the original graph share the same endpoint, then the corresponding vertices in the line graph are adjacent to each other. In other words, the line graph transforms the "edge relationships" in the original graph into new "vertex relationships." If we deploy servers on the vertices of the line graph, a server failure will manifest as a link failure in the original graph.

[0006] For a two-dimensional Torus network T(n,m), if its horizontal edges are denoted as... H(r,c)=((r,c),(r,c+1modm)) Let its vertical side be denoted as V(r,c)=((r,c),(r+1modn,c)) Then the set of edges in the original graph can be written as E(T(n,m))={H(r,c),V(r,c)|0≤r≤n-1,0≤c≤m-1} Since each coordinate position corresponds to one horizontal edge and one vertical edge, there are a total of 2nm edges in T(n,m). Furthermore, the number of vertices in its line graph L(T(n,m)) is also 2nm. Because the original graph T(n,m) is a 4-regular graph, and each endpoint of any edge in the original graph is associated with 3 other edges, the number of vertices adjacent to the vertex corresponding to that edge in the line graph, without double counting, is... (4-1)+(4-1)=6 That is, L(T(n,m)) is a 6-regular graph. This 6-regular structure means that in the linear graph model, each link node has six adjacent candidate expansion directions, thus theoretically providing a structural basis for constructing six vertex independent spanning trees centered on the same common root node.

[0007] However, most existing research on Torus networks focuses on the original Torus graph T(n,m), that is, the research object is mainly the network nodes and their point-to-point connections, rather than the link-level topology on the Torus line graph L(T(n,m)). Although there have been some achievements in constructing vertex spanning trees or multi-path routing on the original graph, these technical solutions are usually difficult to directly transfer to line graph scenarios.

[0008] As can be seen from the background above, although existing technologies have studied the construction of spanning trees, multipath communication, and fault-tolerant broadcasting on two-dimensional Torus networks, most of them are still based on node-level modeling of the original Torus graph. A unified multipath fault-tolerant communication construction scheme oriented towards two-dimensional Torus line graphs and organized around a common root node has not yet been formed. Existing technologies have at least the following drawbacks: They lack a unified explicit construction method for independent vertex spanning trees on the Torus line graph L(T(n,m)) applicable to any n≥3 and m≥3 parameter conditions. Specifically, this includes: 1. The lack of a systematic path organization method around a common root node. If the trunk regions, advancement directions, and root entry channels of different spanning trees are not clearly distinguished, paths between different trees are prone to large-scale overlap, leading to a significant decrease in their fault tolerance. 2. The lack of a unique parent node determination mechanism for branching regions. In practical implementation, some link nodes may have multiple candidate adjacent directions simultaneously. If state distinction or incoming direction distinction rules are not further introduced, the selection of the parent node will not be unique, thereby destroying the acyclicity and connectivity of the spanning tree. 3. There is still a lack of mature and feasible technical solutions for constructing a spanning tree of 6 vertices sharing the same common root node. Summary of the Invention

[0009] The objective of this invention is achieved through the following technical solutions.

[0010] This invention maps a two-dimensional Torus network to a Torus line graph, configures six distinct root gateways around a common root node, and combines the backbone region, backbone direction, root endpoints, and incoming direction determination rules to uniformly construct six spanning trees that share a common root node and satisfy vertex independence, thereby providing multiple independent root paths for any non-root node. Furthermore, by tracing the aforementioned root paths, determining the availability of root paths under the faulty line graph node set, and performing fault-tolerant communication decisions based on the number of available paths, the invention improves the network's communication reliability, stability, and scalability in random link failure environments.

[0011] The present invention adopts the following technical solution: A method for constructing multipath fault-tolerant communication based on Torus line graphs includes the following steps: 1. Obtain the scale parameters n and m of the two-dimensional Torus network, where n≥3 and m≥3.

[0012] 2. Construct a two-dimensional Torus primitive network T(n,m) and represent its vertices as (r,c), where 0≤r≤n-1 and 0≤c≤m-1.

[0013] 3. Denote the horizontal edges in the original network as H(r,c) and the vertical edges as V(r,c), and map each edge in the original network to a node in the Torus line graph L(T(n,m)); if two edges in the original network share an endpoint, then their corresponding line graph nodes are adjacent.

[0014] 4. Select a preset root node in the online graph as the common root node. Prioritize selecting the online graph node corresponding to the horizontal edge H(0,0) connecting the original graph vertex (0,0) and (0,1) as the common root node (Note: H(0,0) represents the horizontal edge starting from row 0 and column 0).

[0015] 5. Among the six adjacent nodes of the above common root node, determine six distinct root gateway nodes. The above six gateway nodes correspond to six independent spanning trees of vertices.

[0016] The gateway and structural parameters of the six spanning trees are configured according to the table below; in this table, H(r,c) represents the horizontal link starting from the r-th row and c-th column, and V(r,c) represents the vertical link starting from the r-th row and c-th column. For the case where m=3, the trunk regions of the first and second trees are degraded to column c=2, and the degradation rules described later are used to resolve conflicts.

[0017]

[0018] 6. Configure the trunk column or trunk region, trunk advancement direction, root endpoint, and lateral merging direction for each of the six spanning trees. Specifically, the trunk regions of the first and second trees are c∈{2,…,m-1}; the trunk columns of the third and fifth trees are c=0; the trunk columns of the fourth and sixth trees are c=1; and two trees sharing the same trunk column or trunk region use opposite advancement directions.

[0019] 7. For any non-root graph node, construct a representative state s=(e,u,tau) in the corresponding tree, where e is the current graph node, u is the endpoint of the edge that e exits from in the original graph, and tau is the direction type when the path enters u; determine a unique parent node based on the region where the current node is located, its main branch, its direction of advancement, and its direction type tau.

[0020] The process of determining the parent node can be represented by the parent node function Father(e,k,n,m), whose inputs include the current line graph node e, the spanning tree number k, and the scale parameters n and m. The output is the unique parent line graph node f of e in the k-th spanning tree. This function first reads the corresponding trunk region, trunk advancement direction, and root entry endpoint based on the tree number k. Then, based on the type of e and the representative state s=(e,u,tau), it determines whether the current state is in the lateral merging stage, trunk advancement stage, or gateway root entry stage. Finally, it outputs the line graph node corresponding to the next original graph edge that shares an endpoint with the current original graph endpoint u.

[0021] Specifically, if the current state has not yet entered the corresponding trunk region, the parent node function selects a horizontal adjacent link that moves it closer to the target trunk region along its current row; if the current state is already in the trunk region, the parent node function selects a vertical adjacent link according to the upward or downward trunk advancement direction configured for the tree; if the current state has entered the neighboring region of the root gateway, the parent node function selects an adjacent link leading to the corresponding root gateway or common root node. For bifurcation positions with two candidate directions, the parent node function determines a unique candidate direction based on the incoming direction type tau, thereby ensuring that each non-root graph node generates only one parent edge in each tree.

[0022] 8. Repeat the parent node determination process for all non-root nodes in the line graph to generate six independent spanning trees with a shared root node.

[0023] 9. For any node to be sent, extract the six root paths from its six independent spanning trees to the common root node.

[0024] 10. Under a given fault scenario, construct a fault line graph node set F, and determine whether the internal line graph node set of each root path intersects with the fault set; when the number of available root paths reaches a preset threshold, determine that the node communication is successful; otherwise, determine that the node communication fails, and further trigger the rerouting strategy.

[0025] When m=3, the parent node selection relationship is redefined using a degradation rule for the conflict column region in order to maintain the uniqueness of the parent edge and the independence of the path.

[0026] In the degenerate case of m=3, column c=2 coincides with c=m-1 in the general case, and some lateral merging regions and trunk boundary regions are merged. At this time, the six root gateways, trunk grouping, and overall path phase structure are not changed. Only the parent edge direction is reassigned for the local regions where columns overlap, so that any representative state still corresponds to a unique parent node, and the root path of each tree still reaches the common root node in the order of "lateral merging - trunk advancement - gateway root entry".

[0027] The advantages of this invention are: it can more directly depict the adjacency relationship between links, making it more suitable for link-level fault analysis; it can uniformly construct 6 independent spanning trees with a unified common point as the root on a two-dimensional Torus graph L(T(n,m)), with 6 root paths between the root and any target vertex that are independent of each other; it can reduce intermediate overlap between different paths and improve fault-tolerant communication capabilities by separating gateways, grouping backbones, and complementing directions; it can ensure the correctness, stability, and feasibility of the algorithm construction through the unique parent node rule and special degradation processing mechanism; and it can unify multi-path construction, path tracing, fault determination, and communication decision-making into the same technical framework, facilitating its application in parallel computing networks, data center interconnection networks, and other surround topology communication systems. Attached Figure Description

[0028] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a schematic diagram of the original two-dimensional Torus network structure. Figure 2 This is a schematic diagram of a two-dimensional Torus line graph structure (the node numbers in the original graph have been simplified). Figure 3 This is a diagram of the common root node and six incoming root gateway nodes. Figure 4 This is a schematic diagram of the structural division of labor among six independent spanning trees. Figure 5 This is a flowchart of the method of the present invention. Figure 6 This is the outgoing edge rule for nodes under the general case where m≥4. Figure 7A This is a schematic diagram of the first independent spanning tree. Figure 7B This is a schematic diagram of the second independent spanning tree. Figure 7C This is a diagram of the third independent spanning tree. Figure 7D This is a schematic diagram of the fourth independent spanning tree. Figure 7E This is a schematic diagram of the fifth independent spanning tree. Figure 7F This is a schematic diagram of the independent spanning tree of the sixth vertex. Figure 8 It is a superimposed graph of six root paths from the same starting point. Figure 9 It is a degeneracy rule for the special case of m=3. Figure 10A This is a schematic diagram of the first independent spanning tree (n=5, m=3). Figure 10B This is a schematic diagram of the second independent spanning tree (n=5, m=3). Figure 10C This is a schematic diagram of the third independent spanning tree (n=5, m=3). Figure 10D This is a schematic diagram of the fourth independent spanning tree (n=5, m=3). Figure 10EThis is a schematic diagram of the fifth independent spanning tree (n=5, m=3). Figure 10F This is a schematic diagram of the sixth independent spanning tree (n=5, m=3). Figure 11 This is a diagram showing the communication performance under different fault conditions. Figure 12 This is an example diagram of the path tracing output. Detailed Implementation

[0029] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0030] Terminology Explanation: Torus network: A two-dimensional, ring-shaped interconnected network in which nodes are connected in a ring-like manner in both the row and column directions.

[0031] Torus Line Graph: A graph that maps communication links in the original Torus graph to nodes and determines the adjacency relationships of nodes in the line graph based on the shared endpoint relationships of the links.

[0032] Independent spanning tree: Given a graph, there are multiple spanning trees on which there is a common root node, and the internal nodes of different paths from any common starting point to the common root node are not shared except for the common root node and the starting point.

[0033] Root gateway: The only adjacent node in a spanning tree before it enters the common root node.

[0034] Parent node / parent edge: The unique next-hop node / edge of a non-root node in a spanning tree that points to the common root node.

[0035] Main region: A column region or set of columns in a spanning tree on a Torus line graph used to guide the horizontal (corresponding to the original graph) input path to the root gateway in the original graph.

[0036] Representative state: An auxiliary state used to uniquely determine the parent node, denoted as s=(e,u,tau), where e is the current line graph node, u is the exit endpoint of the edge corresponding to e in the original graph, and tau is the incoming direction type.

[0037] Fault line diagram node set: The set of failed nodes in the line diagram, whose elements correspond to the failed communication links in the original Torus network.

[0038] like Figure 1As shown, the original 2D Torus network consists of n rows and m columns of nodes connected in loops along the horizontal and vertical directions, where n ≥ 3 and m ≥ 3. Each node in the original network can be represented as (r, c), with horizontal adjacency relationships calculated using c modulo m and vertical adjacency relationships calculated using r modulo n. Since each node has four adjacent directions (left, right, up, and down), the original 2D Torus graph is a 4-regular network.

[0039] like Figure 2 As shown, this invention does not directly use the nodes in the original Torus graph as the objects for constructing the spanning tree. Instead, it first maps each communication link in the original graph to a node in the Torus line graph L(T(n, m)). Specifically, the horizontal link in the original graph is denoted as H(r, c), and the vertical link is denoted as V(r, c). If two links in the original graph share an endpoint, then their corresponding two nodes in the line graph are adjacent. Thus, a node in the line graph corresponds to a link in the original network, and the edges in the line graph represent the shared endpoint relationship between two links. This modeling method can directly analyze link-level failures, link replacements, and edge-level path isolation. To make the illustration more concise, Figure 2 The node numbers in the original Torus graph are simplified. For example, node 0, 0 is simplified to node 0, node 0, 1 is simplified to node 1, node 1, 0 is simplified to 3, and so on, thus simplifying the representation of the graph.

[0040] like Figure 3 As shown, in the online graph L(T(n,m)), the node corresponding to H(0,0) is selected as the common root node. Since L(T(n,m)) is a 6-regular graph, the common root node has six adjacent line graph nodes. In this invention, these six adjacent nodes are used as root gateways for six independent spanning trees, preferably set as g1=H(0,m-1), g2=H(0,1), g3=V(n-1,0), g4=V(n-1,1), g5=V(0,0), and g6=V(0,1). The six gateways correspond to T1 to T6 respectively, ensuring that the paths from each spanning tree to the common root node are distinct.

[0041] like Figure 4As shown, the six spanning trees are structurally divided according to their trunk regions and progression directions. The first tree T1 and the second tree T2 have column regions c=2,...,m-1 as their trunk regions, and their progression directions on the trunks are opposite. The third tree T3 and the fifth tree T5 have column c=0 as their trunk column, and their progression directions are opposite. The fourth tree T4 and the sixth tree T6 have column c=1 as their trunk column, and their progression directions are opposite. For the same starting node, its root path in each tree typically undergoes three stages: "lateral inflow, trunk progression, and gateway entry into the root." Because different trees use different gateways, different trunk columns, or different progression directions, the overlap of nodes within different root paths can be reduced.

[0042] To ensure that each non-root graph node has a unique parent node in each tree, this invention introduces a representative state s=(e,u,tau). Here, e is the current graph node, u is the exit endpoint of the edge corresponding to e in the original graph, and tau represents the incoming direction type when the path enters u. Figure 7A For example, if e is ((0,2),(0,3)), then u is (0,3), and tau is horizontal to the right. The parent node determination module outputs a unique parent edge direction based on the tree number k, the region where the node is located, the trunk direction, the root endpoint, and the incoming direction type tau. If there are multiple candidate directions at a certain local location, the tau is used to distinguish the entry state from the horizontal or vertical link, thereby eliminating ambiguity in the parent node selection.

[0043] like Figure 5 As shown, the method of this invention can be summarized as follows: input scale parameters n and m; construct a two-dimensional Torus original graph T(n,m); map the links in the original graph to Torus line graph nodes; select a common root node. =H(0,0); Configure six root gateways; Determine the parent node of each non-root node according to the trunk region, the direction of advancement, and the type of incoming direction; Generate six independent vertex spanning trees from all parent edges; Extract six root paths from the nodes to be communicated to the common root node; Determine the availability of paths in fault scenarios; Finally, output communication success or communication failure based on the number of available paths, and can further trigger rerouting strategies.

[0044] like Figure 6 As shown, we present the outgoing edge rules for the nodes of the six trees. The direction symbols have the following meanings: →F indicates that the edge to the right is the parent edge, ←S indicates that the edge to the left is not the parent edge, and ↑ and ↓ are similar. If a direction has no outgoing edges, it is not listed. Horizontal edges include horizontal wrapping edges, and vertical edges include vertical wrapping edges. Each non-root state has exactly one parent edge F; if a branching rule with an asterisk appears in the table, the parent edge originating from the type tau is uniquely determined.

[0045] For the special case of m=3, then as follows Figure 9 As shown, in general cases, some column intervals may merge or become empty, potentially leading to conflicts if the rule of m≥4 is still applied. Therefore, this invention re-sets the parent edge selection rule for conflicting columns with m=3, ensuring that each non-root state still has a unique parent node and maintaining the overall path phase structure of "lateral inflow, trunk advancement, and gateway into root." This degradation rule guarantees that the six trees still possess spanning tree properties and path independence under special scales.

[0046] The inventiveness of this invention is mainly reflected in the following aspects: First, it maps the links in the two-dimensional Torus original graph to line graph nodes, constructing a multi-path fault-tolerant communication structure from the link level; Second, it utilizes the 6-regular neighborhood of the common root node in the Torus line graph to configure six distinct incoming root gateways and construct six independent vertex spanning trees sharing the common root node; Third, it determines the unique parent node by jointly identifying the trunk region, trunk direction, incoming root endpoint, and incoming direction type, making the construction rules applicable to both theoretical proof and program implementation; Fourth, it provides conflict resolution rules for the degradation case of m=3, enabling general and special scales to be uniformly incorporated into the same technical framework; Fifth, it integrates spanning tree construction, path tracing, fault injection, availability judgment, and fault-tolerant communication decision-making into an executable, verifiable, and demonstrable network system solution.

[0047] Example 1: Construction of a six-vertex independent spanning tree under normal scale.

[0048] If we take n=4 and m=4, we construct a two-dimensional Torus primitive graph T(4,4). This primitive graph contains 16 original nodes and 32 communication links, therefore its line graph L(T(4,4)) contains 32 line graph nodes. H(0, 0) is the common root node. The six root gateways are then defined as g1=H(0,3), g2=H(0,1), g3=V(3,0), g4=V(3,1), g5=V(0,0), and g6=V(0,1). According to the definitions of H(r, c) and V(r, c), H(0,3) corresponds to... Figure 7A The actual edge is ((0,3),(0,0)), and other vertices are similar. For each non-root node in the line graph, the parent node is determined according to the trunk region from T1 to T6, the direction of advancement, and the type of incoming direction. After determining the parent node for all non-root nodes, six directed spanning trees with H(0, 0) as the common root node are obtained. Figures 7A to 7F Visualizations of the six trees at this scale are presented separately.

[0049] In this embodiment, each of the six trees has 31 edges, covering all line graph nodes except for the common root node. Any non-root line graph node can reach the common root node within a finite number of steps by repeatedly moving along its parent edge in any tree. Since the root gateways of the six trees are different, root paths from the same starting point in the six trees are forcibly separated in the region near the common root node. Furthermore, due to the complementary relationship between the main column and the direction of advancement, the root paths can also maintain strong separation in the middle region.

[0050] Example 2: Degradation treatment under a special scale of m=3.

[0051] With n=5 and m=3, construct the 2D Torus original graph T(5, 3). This original graph contains 15 original nodes and 30 communication links, therefore its line graph L(T(5, 3)) contains 30 line graph nodes. At this time, the column set is only c=0, c=1, c=2. In general, the backbone region of T1 / T2 c=2,...,m-1 degenerates into a single column c=2, and some boundary rules will encounter adjacent column rules. When the parent node is determined, the system calls the m=3 degenerate rule to re-specify the parent edge direction at the conflicting column. Figures 10A to 10F Visualizations of the six trees at this scale are presented separately.

[0052] In this embodiment, the common root node remains H(0, 0), and the six root gateways correspond to H(0, 2), H(0, 1), V(4, 0), V(4, 1), V(0, 0), and V(0, 1), respectively. The degradation rule only changes the selection of the parent edge at the conflict location; it does not change the global organization of the six trees, nor does it change the requirement that each tree enters the common root node through a unique gateway. Therefore, each non-root graph node still has a unique parent node in each tree, and the six trees can still cover all graph nodes and remain pairwise independent.

[0053] Example 3: Fault-tolerant communication determination in fault scenarios.

[0054] For any given sizes n and m, the system first constructs six independent spanning trees and caches the six root paths from T1 to T6 to the common root node for each non-root graph node. Let the fault set be F, where the elements of F are the faulty graph nodes, i.e., the faulty links in the original Torus network. For a given starting node x, the system sequentially checks whether the internal nodes of paths P1(x), P2(x), ..., P6(x) intersect with F. If the set of internal nodes of a path does not intersect with F, the path is considered usable; if the number of usable paths reaches a preset threshold q, the communication from node x to the common root node is considered successful. Furthermore, q is set to 3, meaning that communication is considered successful when at least three root paths are available.

[0055] Figure 8 This demonstrates the effect of root path stacking in six trees with the same starting node. It can be seen that although the six paths share the same common root node, they employ different channel organization methods in the middle region and the root entry region, thereby reducing the probability of multiple faulty nodes simultaneously blocking all paths.

[0056] Example 4: System Visualization and Programmatic Implementation.

[0057] In one executable implementation, the system uses Python, NetworkX, and Matplotlib to build an interactive verification platform. After the user inputs n and m, the network modeling module generates the original Torus graph and the Torus line graph; the tree construction module generates T1 to T6 according to the parent node determination rules; each tree structure is displayed in different colors (see Figures 7 and 10 above); the path tracing module receives the starting edge endpoint and outputs the path sequence from the starting line graph node to the common root node (see Figure 10 above). Figure 12 The fault injection module generates a random set of faults; the fault tolerance decision module outputs the communication success rate, the number of available paths, or rerouting prompts. This implementation can be used as an algorithm component in software systems, simulation platforms, or network controllers.

[0058] In another implementation, the system can pre-cachate the internal node sets of six root paths P1(x) to P6(x) for each non-root graph node x. When the fault set F is updated, there is no need to reconstruct the spanning tree; the path availability can be obtained simply by determining whether each internal node set intersects with F. This caching mechanism can transform a single fault determination into a set intersection operation, making it suitable for repeated use in network controllers, fault-tolerant broadcast schedulers, or simulation platforms.

[0059] To verify the correctness and fault tolerance of the technical solution of this invention, automated checks were performed on all scales within the range of 3≤n≤20 and 3≤m≤20. The checks included: whether each spanning tree covers all nodes in the line graph; whether each tree is acyclic and connected; whether each non-root line graph node can be traced along its parent edge to a common root node; and whether the paths between any two trees from the same starting point to the common root node have no common internal line graph nodes other than the common root node. The verification results show that, within the above parameter range, all six trees constructed by this invention satisfy the requirements of spanning tree properties and path independence.

[0060] Furthermore, Monte Carlo simulation experiments were used to evaluate communication performance under fault conditions. The experiment treated Torus line graph node failures as link failures in the original Torus network; the failure rate p was set in increments of 3% within the range of 0% to 30%; 800 independent randomized experiments were performed at each failure rate level, repeated for 30 rounds. The test networks included the original horizontal expansion groups T(4, 3), T(4, 4), T(4, 5), T(4, 6), and the original vertical expansion groups T(3, 4), T(4, 4), T(5, 4), T(6, 4). The communication success criterion was that at least three of the six root paths originating from the same point in time were available.

[0061] Experimental results are as follows Figure 11 The results show that when the failure rate is below 6%, the communication success rate of all tested networks remains at 100%. When the failure rate rises to 21%, the T(4, 3) scale still maintains a communication success rate of approximately 83%, while the T(4, 6) scale maintains approximately 55%. When the failure rate rises to 30%, the communication success rate of the T(4, 3) scale is approximately 53%, while the T(4, 6) scale is approximately 29%. The trends under horizontal and vertical scaling are basically consistent. After scaling from T(4, 4) to T(4, 6) or T(6, 4), the deviation in success rate at each failure rate level is controlled within approximately 3 percentage points. The fluctuation range of the mean at each point in 30 rounds of repeated experiments is generally controlled within 2%, indicating that the experimental results have good stability.

[0062] The above results demonstrate that the six independent spanning trees of this invention can provide strong multipath redundancy in low-failure-rate environments, and can still maintain a certain proportion of available communication paths in medium-to-high-failure-rate environments. Furthermore, the algorithm exhibits good consistency in both horizontal and vertical expansion. Compared to multipath schemes that construct only a single spanning tree or do not distinguish the root path, this invention can improve link-level fault-tolerant communication capabilities through gateway separation, backbone division of labor, and path independence.

[0063] The experimental parameters described above are used to illustrate the effectiveness of the present invention and do not constitute a limitation on the scope of protection. In practical applications, the values ​​of n and m, the failure rate range, the number of repeated experiments, the communication success threshold, and the failure generation method can all be adjusted according to the specific network scale and reliability requirements.

[0064] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for constructing multipath fault-tolerant communication based on Torus line graphs, characterized in that, Includes the following steps: Construct a Torus line graph, mapping the communication links in the original two-dimensional Torus network to line graph nodes, and establishing adjacency relationships between line graph nodes based on the endpoint sharing relationships between links in the original network; In the online graph, a preset node is selected as the common root node, and multiple distinct root gateway nodes are determined among the adjacent nodes of the common root node. Each of the multiple root gateway nodes corresponds to a set of independent vertex spanning trees. For each set of independent vertex spanning trees, a trunk region, a trunk propagation direction, and an ingress endpoint are configured, wherein the trunk propagation directions of two spanning trees sharing the same trunk region are opposite; For any non-root line graph node, in each spanning tree, the parent node of the current node in the spanning tree is uniquely determined according to the current node's location, the corresponding main trunk advancement direction, and the incoming direction type, based on the preset parent node determination rules. Generate a set of independent spanning trees for vertices, including the common root node, based on the parent-child relationships of all non-root nodes; For the node to be sent, extract its multiple root paths to the common root node in each vertex's independent spanning tree; Given a fault scenario, determine whether the internal nodes of each root path intersect with the set of faulty nodes, and make a communication decision based on the relationship between the number of available root paths and a preset threshold.

2. The method according to claim 1, characterized in that, The preset parent node determination rules include: If the current state has not yet entered the corresponding backbone region, then select the lateral adjacent link that moves it closer to the target backbone region as the parent edge; If the current state is already in the trunk region, then select the vertically adjacent link as the parent edge according to the trunk advancement direction configured in this tree; If the current state has entered the neighboring domain of the root gateway, then select the adjacent link leading to the corresponding root gateway or common root node as the parent edge. At a fork location with multiple candidate directions, the parent edge direction is uniquely determined based on the type of the incoming direction.

3. The method according to claim 1, characterized in that, The number of the multiple root gateway nodes is six, and the number of the set of independent vertex spanning trees is six, wherein two spanning trees share the first trunk region and advance in opposite directions, two spanning trees share the second trunk column and advance in opposite directions, and the other two spanning trees share the third trunk column and advance in opposite directions.

4. The method according to claim 1, characterized in that, When the network size parameters meet the preset degradation conditions, the degradation rules are used to reassign the parent edge direction to the conflict area to ensure that each non-root graph node still has a unique parent node in each tree.

5. The method according to claim 1, characterized in that, The preset threshold is when the number of available root paths is greater than or equal to half of the total number of root paths.

6. The method according to claim 1, characterized in that, The method further includes: caching the internal node set of multiple root paths for each non-root line graph node, and determining the path availability by performing a set intersection operation when the faulty node set is updated.

7. A multipath fault-tolerant communication system based on Torus line graphs, characterized in that, include: The line graph mapping module is used to map communication links in the original two-dimensional Torus network to line graph nodes, and to establish adjacency relationships between line graph nodes based on the endpoint sharing relationship between links. The root node and gateway configuration module is used to select a preset node as a common root node in the online graph, and determine multiple distinct root gateway nodes among the adjacent nodes of the common root node, each corresponding to a set of independent spanning trees of vertices; The trunk configuration module is used to configure the trunk region, trunk advancement direction and root endpoint for the set of independent vertex spanning trees respectively, wherein the trunk advancement directions of two spanning trees sharing the same trunk region are opposite; The parent node determination module is used to uniquely determine the parent node of any non-root line graph node in each spanning tree based on the current node's location, the corresponding main trunk advancement direction, and the incoming direction type, according to the parent node determination rules. A spanning tree construction module is used to generate an independent spanning tree of vertices, including the common root node, based on the parent-child relationships of all non-root nodes. The path extraction module is used to extract multiple root paths from the node to be sent to the common root node in each spanning tree; The fault-tolerant communication decision module is used to determine whether the internal nodes of each root path intersect with the set of faulty nodes given a set of faulty nodes, and to make communication decisions based on the relationship between the number of available root paths and a preset threshold.

8. The system according to claim 7, characterized in that, The parent node determination module is specifically used for: If the current state has not yet entered the corresponding backbone area, then select the lateral adjacent link that is closer to the target backbone area as the parent edge; If the current state is already in the trunk region, then select the vertically adjacent link as the parent edge according to the trunk advancement direction configured in this tree; If the current state has entered the neighboring domain of the root gateway, then select the adjacent link leading to the corresponding root gateway or common root node as the parent edge. At a fork location with multiple candidate directions, the parent edge direction is uniquely determined based on the type of the incoming direction.

9. The system according to claim 7, characterized in that, It also includes a degradation processing module, which, when the network size parameters meet the preset degradation conditions, uses degradation rules to reassign the parent edge direction to the conflict area, maintaining the uniqueness of the parent node of each non-root node.

10. The system according to claim 7, characterized in that, It also includes a path caching module, which caches the set of internal nodes of multiple root paths of each non-root line graph node, so that the fault-tolerant communication decision module can quickly determine availability through set operations.

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