CN116846820A - Fault-tolerant routing algorithm based on condition of 1 extra connectivity - Google Patents

Abstract

The invention relates to the technical field of data center network fault tolerance, in particular to a fault-tolerant routing algorithm based on a 1-extra connectivity condition, which is applicable to a correction bubbling ordering network MB of a data center network _n . In this algorithm, MB _n The number of the fault vertexes is smaller than 1, and after the fault vertexes are deleted, at least 2 non-fault vertexes exist in each sub-graph. The algorithm can find a fault-free path between any two fault-free vertices in each branch, wherein 1 extra connectivity is also called 1-extra connectivity. When some routes in the network fail, the algorithm can automatically calculate an alternative path to ensure the normal operation of the network, and the stability and fault tolerance of the network can be improved.

Description

Fault-tolerant routing algorithm based on condition of 1 extra connectivity

Technical Field

The invention relates to the technical field of data center network fault tolerance, in particular to a fault-tolerant routing algorithm based on a condition of 1 extra connectivity.

Background

As the number of processors in a network increases, the probability of a processor failing increases. When a processor in a network fails, whether certain characteristics in the network continue to depend on the fault tolerance of the network is a key indicator for measuring the quality of the interconnection network. In recent years, the fault tolerance problem of interconnection networks has been a hotspot for researchers to study. The vertex connectivity is an important parameter for measuring network fault tolerance. Moreover, in a network where some processors fail and remain connected after deletion, how to route between the processors without failure is an important issue to consider in studying the fault tolerance of the network, which is called a fault tolerant routing problem. While merely measuring the fault tolerance of a network by vertex connectivity is still deficient, for example, for some common network structures, the vertex connectivity is at most the minimum of the number of neighbors of all vertices in the network. In this case, the probability that all neighbors of a certain vertex fail at the same time is extremely small, especially when the size of G is large enough, the probability that this occurs approaches 0. Therefore, the conventional vertex connectivity does not scale well to the quality of the actual interconnect network fault tolerance.

Disclosure of Invention

The summary of the invention is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. The summary of the invention is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

In order to solve the fault-tolerant routing problem, the invention provides a fault-tolerant routing algorithm based on the condition of 1 additional connectivity.

The invention provides a fault-tolerant routing algorithm based on a condition of 1 extra connectivity, which comprises the following steps:

determining a departure vertex x and a destination vertex y, and judging a subgraph MB ^α _n Sum-sub picture MB ^β _n Whether or not it is the same sub-graph, wherein the departure vertex x is located in sub-graph MB ^α _n In which the destination vertex y is located in sub-picture MB ^β _n In (a) and (b);

if α is not equal to β, then determine |F _α |、|F _β I and kappa (MB) _n ) And invoking a corresponding method to obtain a total path under the corresponding condition, wherein,the total path is a path formed by fault-free paths, the starting point of the total path is a departure vertex x, and the end point of the total path is a destination vertex y;

if α=β, then determine |f _α＝β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

Optionally, the judging |F _α |、|F _β I and kappa (MB) _n ) And calling a corresponding method to obtain a total path under the corresponding condition, comprising:

if |F _α |≥κ(MB _n ) Then the PATHSEQ method is called to obtain the departure vertex x from the sub-graph MB ^α n reaches G-MB ^α _n Any vertex z ₁ Is not failed path P of (1) ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is vertex z ₁ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is not the vertex z ₁ Then the MBVP method is called to obtain the sub-graph G-MB ^α Vertex z in n ₁ Failure-free path P to destination vertex y ₂ The method comprises the steps of carrying out a first treatment on the surface of the The total path is obtained as (P ₁ ，P ₂ )；

If |F _β |≥κ(MB _n ) Then the PATHSEQ method is called to obtain the destination vertex y from sub-graph MB ^β _n Reach G-MB ^β _n Any vertex z ₂ Is not failed path P of (1) ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the departure vertex x is vertex z ₂ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the departure vertex x is not the vertex z ₂ Then the MBVP method is called to obtain the sub-graph G-MB ^β Departure vertex x reaches vertex z in n ₂ Is not failed path P of (1) ₂ The method comprises the steps of carrying out a first treatment on the surface of the The total path is obtained as (P ₂ ，P ₁ ^-1 ) Wherein P is ₁ ^-1 Is P ₁ Is a reverse path of (a);

if |F _α |<κ(MB _n ) And |F _β |<κ(MB _n ) Then the PATHSEQ method is called to obtain the departure vertex x from the sub-graph MB ^α n reaches MB ^β _n Any vertex z ₃ Is not failed path P of (1) ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is vertex z ₃ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertexy is not the vertex z ₃ Then call MBVP method to get in-sub-picture MB ^β _n Middle vertex z ₃ Failure-free path P to destination vertex y ₂ The method comprises the steps of carrying out a first treatment on the surface of the The total path is obtained as (P ₁ ，P ₂ )。

Optionally, the judging |F _α＝β I and kappa (MB) _n ) And calling a corresponding method to obtain a total path under the corresponding condition, comprising:

if |F _α＝β |<κ(MB _n ) Then call MBVP to get in-sub-picture MB ^α In n, the departure vertex x reaches a fault-free path P of the destination vertex y, and the fault-free path P is taken as a total path;

if |F _α＝β |≥κ(MB _n ) Then call PATHSEQ to get departure vertex x from sub-graph MB ^α n reaches G-MB ^α _n Failure-free path P of any vertex s ₁ The method comprises the steps of carrying out a first treatment on the surface of the Invoking PATHSEQ to obtain destination vertex y from sub-graph MB ^β _n Reach G-MB ^β _n Failure-free path P of any vertex h ₂ The method comprises the steps of carrying out a first treatment on the surface of the If P ₁ And P ₂ With common vertices, let the first common vertex be vertex z, and the total Path be (Path (P) ₁ ，x，z)，Path(P ₂ ^-1 Z, y)); if P ₁ And P ₂ Without common vertices, invoking MBVP gets in sub-graph G-MB ^α _n Failure-free path P of middle vertex s to vertex h ₃ The total path was obtained as (P ₁ ，P ₃ ，P ₂ ^-1 )。

The invention has the following beneficial effects:

the invention can quickly find a fault-free path between any two fault-free peaks under the condition of some peak faults, improves the stability and fault tolerance of the network, and ensures the continuity and normal operation of the network. The modified bubbling ordering network has wide application prospect in the fields of data centers, high-performance computation and the like, has better network performance and reliability, and is easy to realize and operate and maintain. The modified bubbling ordering network is a network topology structure with very good locality, and only short-distance links exist between nodes, so that delay in the network can be effectively reduced. The multi-channel parallel link processing system has a plurality of parallel links, can process a plurality of data simultaneously, and has high bandwidth and throughput. The correction bubbling ordering network is easy to realize and deploy, the construction and operation cost of the network can be effectively reduced, the topological structure is flexible, the expansion and adjustment can be carried out according to the needs, and the network has good expandability. The conventional vertex connectivity does not measure the quality of the fault tolerance of the actual interconnection network well. To solve this problem, F' abrega and Fiol define g-extra connectivity based on the concept of conditional connectivity. After requiring the deletion of the failed vertices in the network, each branch remaining contains at least g+1 non-failed vertices.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions and advantages of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of a fault tolerant routing algorithm based on the condition of 1 additional connectivity according to the present invention;

FIG. 2 is a further flowchart of the present invention;

FIG. 3 is a schematic diagram of a modified bubble ordering network MB of the present invention ₄ A schematic structural diagram.

Detailed Description

In order to further describe the technical means and effects adopted by the present invention to achieve the preset purpose, the following detailed description is given below of the specific implementation, structure, features and effects of the technical solution according to the present invention with reference to the accompanying drawings and preferred embodiments. In the following description, different "one embodiment" or "another embodiment" means that the embodiments are not necessarily the same. Furthermore, the particular features, structures, or characteristics of one or more embodiments may be combined in any suitable manner.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

The invention provides a fault-tolerant routing algorithm based on a condition of 1 extra connectivity, which comprises the following steps:

the degree of vertex connectivity of G is the minimum number of vertices that need to be removed to render G unconnected or trivial, denoted by k (G). Let MB ^j _n For the vertex set { u } _n u _n-1 ...u ₂ j, where j e<n>\{0}；MB ^J _n Is U-shaped _j∈J V(MB ^j _n ) Derived subgraph, whereinFor any one vertex set +.>Let F _j ＝F∩V(MB ^j _n )，F _J ＝∪ _j∈J F _j ，|F _J I is set F _J Is a number of (a) in the number of (b) in the number of (a).

Determining a departure vertex x and a destination vertex y, and judging a subgraph MB ^α _n Sum-sub picture MB ^β _n Whether it is the same subgraph;

if α is not equal to β, then determine |F _α |、|F _β I and kappa (MB) _n ) And calling a corresponding method to obtain a total path under a corresponding condition;

if α=β, then determine |f _α＝β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

The following detailed development of each step is performed:

referring to fig. 1, a flow of some embodiments of a fault-tolerant routing algorithm based on a 1-extra connectivity condition according to the present invention is shown. The fault-tolerant routing algorithm based on the condition of 1 additional connectivity comprises the following steps:

step S1, determining a departure vertex x and a destination vertexy, judge sub-picture MB ^α _n Sum-sub picture MB ^β _n Whether it is the same sub-graph.

In some embodiments, departure vertex x and destination vertex y may be determined, and subgraph MB may be determined ^α _n Sum-sub picture MB ^β _n Whether it is the same sub-graph.

Wherein the departure vertex x is located in the sub-picture MB ^α _n Is a kind of medium. The destination vertex y is located in sub-picture MB ^β _n Is a kind of medium.

As an example, a departure vertex x and a destination vertex y may be determined, the departure vertex x being located in the subgraph MB ^α _n The destination vertex y is located in sub-picture MB ^β _n Is a kind of medium. Judging MB ^α _n And MB (MB) ^β _n If the sub-graph is the same sub-graph, if the alpha is not equal to the beta, executing the step S2; conversely, if α=β, step S3 is performed.

A further flow chart of the present invention may be as shown in fig. 2, taking as an example a modified bubble ordering network, the modified bubble ordering network structure when n=4 may be as shown in fig. 3.

Step S2, if α is not equal to β, judging |F _α |、|F _β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

In some embodiments, if α+.β, then |F can be determined _α |、|F _β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

The total path is a path formed by fault-free vertexes, the starting point of the total path is a departure vertex x, and the end point of the total path is a destination vertex y.

As an example, if α+.β, then determine |f _α |、|F _β I and kappa (MB) _n ) The step of calling different methods to obtain paths under various conditions can comprise the following steps:

first, if |F _α |≥κ(MB _n ) Then the PATHSEQ method is called to obtain the departure vertex x from the sub-graph MB ^α n reaches G-MB ^α _n Any one of the topsPoint z ₁ Is not failed path P of (1) ₁ . If the destination vertex y is vertex z ₁ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is not the vertex z ₁ Then the MBVP method is called to obtain the sub-graph G-MB ^α Vertex z in n ₁ Failure-free path P to destination vertex y ₂ . Thus, the total path is (P ₁ ，P ₂ )。

Second step, if |F _β |≥κ(MB _n ) Then the PATHSEQ method is called to obtain the destination vertex y from sub-graph MB ^β _n Reach G-MB ^β _n Any vertex z ₂ Is not failed path P of (1) ₁ . If the departure vertex x is vertex z ₂ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the departure vertex x is not the vertex z ₂ Then the MBVP method is called to obtain the sub-graph G-MB ^β Departure vertex x reaches vertex z in n ₂ Is not failed path P of (1) ₂ . Thus, the total path is (P ₂ ，P ₁ ^-1 ) Wherein P is ₁ ^-1 Is P ₁ I.e. the path from vertex z to vertex y.

Third step, if |F _α |<κ(MB _n ) And |F _β |<κ(MB _n ) I.e. |F _α |<κ(MB _n )&&|F _β |<κ(MB _n ) Then the PATHSEQ method is called to obtain the departure vertex x from the sub-graph MB ^α n reaches MB ^β _n Any vertex z ₃ Is not failed path P of (1) ₁ . If the destination vertex y is vertex z ₃ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is not the vertex z ₃ Then call MBVP method to get in-sub-picture MB ^β _n Middle vertex z ₃ Failure-free path P to destination vertex y ₂ . Thus, the total path is (P ₁ ，P ₂ )。

Step S3, if α=β, judging |f _α＝β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

In some embodiments, if α=β, then |f can be determined _α＝β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

As an example, if α=β, the judgment is |f _α＝β I and kappa (MB) _n ) The step of calling different methods to obtain paths under various conditions can comprise the following steps:

first, if |F _α＝β |<κ(MB _n ) Then call MBVP to get in-sub-picture MB ^α And n, the departure vertex x reaches the non-fault path P of the destination vertex y, and the non-fault path P is taken as a total path.

Second step, if |F _α＝β |≥κ(MB _n ) Then call PATHSEQ to get departure vertex x from sub-graph MB ^α n reaches G-MB ^α _n Failure-free path P of any vertex s ₁ . Re-invoking PATHSEQ to obtain destination vertex y from sub-graph MB ^β _n Reach G-MB ^β _n Failure-free path P of any vertex h ₂ . If P ₁ And P ₂ With common vertices, the first common vertex is made vertex z, so the total Path is (Path (P) ₁ ，x，z)，Path(P ₂ ^-1 Z, y)), where Path (P) ₁ X, z) is path P ₁ Path from vertex x to vertex z, path (P ₂ ^-1 Z, y) is path P ₂ ^-1 From vertex z to vertex y. If P ₁ And P ₂ Without common vertices, invoking MBVP gets in sub-graph G-MB ^α _n Failure-free path P of middle vertex s to vertex h ₃ Thus, the total path is obtained as (P ₁ ，P ₃ ，P ₂ ^-1 )。

Whereby a failure-free path between any two failure-free vertices can be found in each branch. The whole method is named as MBEVP, and the pseudo code corresponding to the MBEVP can be shown in table 1.

TABLE 1

The pseudo code corresponding to PATHSEQ may be as shown in Table 2.

TABLE 2

The pseudo code corresponding to MBVP may be as shown in table 3.

TABLE 3 Table 3

It should be noted that, regarding the time complexity analysis, the function PATHSEQ (x, F, H is first applied to the time complexity of MBEVP ₁ ，H ₂ ) And MBVP (x, y, G, F). For the function PATHSEQ (x, F, H ₁ ，H ₂ ) Wherein H is ₁ And H ₂ Is two subgraphs of G and x is in subgraph H ₁ Is a kind of medium. Depending on the situation, the function may give x to subgraph H ₂ Path (x, x) ₁ )、(x，x ₂ ，x ₃ ) Or (x, x) ₁ ，x ₂ ，x ₃ ). The time complexity of the execution of the PATHSEQ under different conditions is as follows:

case 1, the resulting path is (x, x ₁ ). If it isThe function is derived from (N _G (x)∩V(H ₂ ) Selecting a vertex x from \F ₁ The final return path (x, x ₁ ). The time complexity in this case is O (1).

Case 2, the resulting path is (x, x ₂ ，x ₃ ). The function first traverses the set (N _G (x)∩V(H ₁ ) F), let each vertex in the set be x ₂ Then from (N) _G (x)∩V(H ₂ ) Selecting a vertex x3 from \f, and finally returning the path (x, x) ₂ ，x ₃ ). The temporal complexity in this case is O (|n) _G (x)∩V(H ₁ )|)≤O(n)。

Case 3, the resulting path is (x, x ₁ ，x ₂ ，x ₃ ). In this case, the function is first calculated from (N _G (x)∩V(H ₁ ) Selecting a vertex x from \F ₁ And take the set S≡N _G (x ₁ ∩V(H ₁ ))\(F∪N _G (x)∩V(H ₁ ))). The time complexity of this process is O (1). Then the function will traverse the set S, let x ₂ Is any vertex in set S. Thereafter from (N) _G (x ₂ )∩V(H ₂ ) Selecting a vertex x from \F ₃ The final return path (x, x ₁ ，x ₂ ，x ₃ ). The time complexity in this case is O (|S|) +.O (n).

The functions PATHSEQ (x, F, H) can be obtained by combining case 1, case 2 and case 3 ₁ ，H ₂ ) Is O (n).

Next, the temporal complexity of the function MBVP (x, y, G, F) is analyzed. The function first calls the function buildpath set (MB) _n X, y) to obtain n disjoint paths of x and y in G-F. The time complexity of the process is O (n ³ ). The function MBVP then traverses these disjoint paths to find a fault-free path. If it is determined whether a path is a fault-free path, it is necessary to determine whether each vertex in the path is in the fault set F. The time complexity of this process is O (n). Since invoking the buildpath set results in n paths in total, this determination is performed up to n times. In summary, the time complexity of finding a fault-free path is O (n ³ )×O(n)＝O(n ⁴ )。

Finally, the temporal complexity of the MBEVP was analyzed. The temporal complexity of the MBEVP in both cases α+.β and α=β is as follows:

case 1, when α+.β, can include the following 3 seed cases:

sub-case 1, when |F _α |≥κ(MB _n ) When MBEVP first passes PATHSEQ (x, F, MB) ^α n，G-MB ^α n) obtaining a sequence from u to G-MB ^α P of vertex z in n ₁ The time complexity of this process is O (n). Then, if z=y, then the MBEVP returns to P ₁ . Thus, a fault-free path P is obtained in G-F for x and y ₁ Is O (n). If z+.y, MBEVP returns to path (P ₁ ，MBVP(z，y，G-MB ^α n，F\F _α )). This procedure requires that the function MBVP (z, y, G-MB) is called first ^α n，F\F _α ) Constructing a fault-free path with a time complexity of O (n ⁴ ). Then splice P ₁ And MBVP as described above (z, y, G-MB) ^α n，F\F _α ) The time complexity of the process is O (1) for the constructed fault-free path. Thus, the time complexity of obtaining a fault-free path of x and y in G-F is O (n) +O (n ⁴ )+O(1)≤O(n ⁴ )。

Sub-case 2, when |F _β |≥κ(MB _n ) At this time, similar to the discussion in sub-scenario 1 included in scenario 1, the time complexity of the failure-free paths resulting in x and y in G-F is O (n ⁴ )。

Sub-case 3, when |F _α |<κ(MB _n )&&|F _β |<κ(MB _n ) At this time, similar to the discussion in sub-scenario 1 included in scenario 1, the time complexity of the failure-free paths resulting in x and y in G-F is O (n ⁴ )。

Case 2, when α=β, may include the following 2 seed cases:

sub-case 1, when |F _α |<κ(MB _n ) In this case, MBEVP will directly invoke the algorithm MBVP (x, y, MB) ^α n，F _α ) Constructing a fault-free path, the time complexity of the process is O (n ⁴ )。

Sub-case 2, when |F _α |≥κ(MB _n ) When MBEVP will first call the PATHSEQ function to get a sub-graph from xG-MB ^α Failure-free path P of s in n ₁ And a segment from y to sub-picture G-MB ^α Failure-free path P for vertex h in n ₂ . Here P is obtained ₁ And P ₂ The time complexity of (a) is O (n), respectively. Then, if P ₁ And P ₂ Let z be the first common vertex, then the MBEVP returns the Path (P ₁ ，x，z)，Path(P ₂ ^-1 Z, y)). Because of P ₁ And P ₂ At most dist (x, y) +2 vertices, so the time complexity of obtaining a common vertex z is O (|V (P) ₁ )|×|V(P ₂ )|)≤O((dist(x，y)+2)×(dist(x，y)+2))≤O(n ² ). Because the path (P) ₁ The time complexity of x, z) is O (1), thus a fault-free Path (Path (P1, x, z), path (P) ₂ ^-1 Z, y)) is O (2 n) +o (n) ² )≤O(n ² ). If P ₁ And P ₂ Without a common vertex, MBEVP would return a path (P ₁ ，MBVP(s，h，G-MB ^α n，F\F _α )，P ₂ ^-1 ). The process will call the algorithm MBVP (s, h, G-MB first ^α n，F\F _α ) Constructing a fault-free path with a temporal complexity of O (n ⁴ ). Then splice P ₁ MBVP (s, h, G-MB) as described above ^α n，F\F _α ) Constructed fault-free path and P ₂ ^-1 The time complexity of this process is O (1). Thus, a fault-free path (P ₁ ，MBVP(s，h，G-MB ^α n，F\F _α )，P ₂ ^-1 ) Is of the temporal complexity O (2 n) ² )+O(n ⁴ )+O(1)≤O(n ⁴ )。

Combining all the above cases and situations, the time complexity of MBEVP is O (n ⁴ )。

In summary, the invention can quickly find a fault-free path between any two fault-free peaks under the condition of some peak faults, thereby improving the stability and fault tolerance of the network and ensuring the continuity and normal operation of the network.

The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention and are intended to be included within the scope of the invention.

Claims (3)

1. A fault tolerant routing algorithm based on the condition of 1 additional connectivity, comprising the steps of:

determining a departure vertex x and a destination vertex y, and judging a subgraph MB ^α _n Sum-sub picture MB ^β _n Whether or not it is the same sub-graph, wherein the departure vertex x is located in sub-graph MB ^α _n In which the destination vertex y is located in sub-picture MB ^β _n In (a) and (b);

if α is not equal to β, then determine |F _α |、|F _β I and kappa (MB) _n ) And calling a corresponding method to obtain a total path under a corresponding condition, wherein the total path is a path formed by a fault-free path, the starting point of the total path is a departure vertex x, and the end point of the total path is a destination vertex y;

if α=β, then determine |f _α＝β I and kappa (MB) _n ) And calling the corresponding method to obtain the total path under the corresponding condition.

2. The fault-tolerant routing algorithm based on the condition of 1-extra connectivity according to claim 1, wherein the determination |f _α |、|F _β I and kappa (MB) _n ) And calling a corresponding method to obtain a total path under the corresponding condition, comprising:

if |F _α |≥κ(MB _n ) Then the PATHSEQ method is called to obtain the departure vertex x from the sub-graph MB ^α n reaches G-MB ^α _n Any vertex z ₁ Is not failed path P of (1) ₁ The method comprises the steps of carrying out a first treatment on the surface of the If purpose is toVertex y is vertex z ₁ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is not the vertex z ₁ Then the MBVP method is called to obtain the sub-graph G-MB ^α Vertex z in n ₁ Failure-free path P to destination vertex y ₂ The method comprises the steps of carrying out a first treatment on the surface of the The total path is obtained as (P ₁ ，P ₂ )；

If |F _β |≥κ(MB _n ) Then the PATHSEQ method is called to obtain the destination vertex y from sub-graph MB ^β _n Reach G-MB ^β _n Any vertex z ₂ Is not failed path P of (1) ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the departure vertex x is vertex z ₂ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the departure vertex x is not the vertex z ₂ Then the MBVP method is called to obtain the sub-graph G-MB ^β Departure vertex x reaches vertex z in n ₂ Is not failed path P of (1) ₂ The method comprises the steps of carrying out a first treatment on the surface of the The total path is obtained as (P ₂ ，P ₁ ^-1 ) Wherein P is ₁ ^-1 Is P ₁ Is a reverse path of (a);

if |F _α |<κ(MB _n ) And |F _β |<κ(MB _n ) Then the PATHSEQ method is called to obtain the departure vertex x from the sub-graph MB ^α n reaches MB ^β _n Any vertex z ₃ Is not failed path P of (1) ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is vertex z ₃ The total path is P ₁ The method comprises the steps of carrying out a first treatment on the surface of the If the destination vertex y is not the vertex z ₃ Then call MBVP method to get in-sub-picture MB ^β _n Middle vertex z ₃ Failure-free path P to destination vertex y ₂ The method comprises the steps of carrying out a first treatment on the surface of the The total path is obtained as (P ₁ ，P ₂ )。

3. The fault-tolerant routing algorithm based on the condition of 1-extra connectivity according to claim 1, wherein the determination |f _α＝β I and kappa (MB) _n ) And calling a corresponding method to obtain a total path under the corresponding condition, comprising:

if |F _α＝β |<κ(MB _n ) Then call MBVP to get in-sub-picture MB ^α A non-fault path P from the departure vertex x to the destination vertex y in n is taken asIs the total path;

if |F _α＝β |≥κ(MB _n ) Then call PATHSEQ to get departure vertex x from sub-graph MB ^α n reaches G-MB ^α _n Failure-free path P of any vertex s ₁ The method comprises the steps of carrying out a first treatment on the surface of the Invoking PATHSEQ to obtain destination vertex y from sub-graph MB ^β _n Reach G-MB ^β _n Failure-free path P of any vertex h ₂ The method comprises the steps of carrying out a first treatment on the surface of the If P ₁ And P ₂ With common vertices, let the first common vertex be vertex z, and the total Path be (Path (P) ₁ ，x，z)，Path(P ₂ ^-1 Z, y)); if P ₁ And P ₂ Without common vertices, invoking MBVP gets in sub-graph G-MB ^α _n Failure-free path P of middle vertex s to vertex h ₃ The total path was obtained as (P ₁ ，P ₃ ，P ₂ ^-1 )。