CN114826931A - Method, device, equipment and storage medium for determining fault tolerance of alternate group network structure - Google Patents
Method, device, equipment and storage medium for determining fault tolerance of alternate group network structure Download PDFInfo
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Abstract
The application relates to a method, a device, equipment and a storage medium for determining the fault tolerance of an alternate group network structure, belonging to the technical field of computers, wherein the method comprises the following steps: determining independent vertices in an alternate group network; determining a first neighbor set of the independent vertex; determining a second neighbor set corresponding to the appointed vertex in the first neighbor set; for the designated vertex and the second neighbor set corresponding to the designated vertex, K of the designated vertex is determined 1，t A structure set; determining K of alternate group network according to size of structure set 1，t -structural connectivity and a sub-structural connectivity upper bound; using K 1，t -the structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network. The structure fault tolerance can be determined from the dimension of the structure, and the determination efficiency of the network structure fault tolerance is improved.
Description
Technical Field
The application relates to a method, a device, equipment and a storage medium for determining fault tolerance of an alternate group network structure, and belongs to the technical field of computers.
Background
High-performance parallel computers play an increasingly important role in scientific research, education of petroleum meteorology and other related fields. As high performance parallel computers continue to increase, the number of processors (processors) they own becomes increasingly large. The Network obtained by connecting several processors in a specific manner is called an Interconnection Network (Interconnection Network), and an Interconnection Network can be represented by a simple graph G ═ v (G), e (e)). Where V (G) represents the set of vertices of graph G, and E (G) represents the set of edges of graph G. The vertices in graph G represent processor nodes in the interconnection network, and the edges represent connecting links between the processor nodes. While alternate groups are a typical interconnection network topology.
The conventional alternate group network fault tolerance determining method comprises the following steps: and determining whether the alternate group networks are connected or not by deleting the fault vertexes in the alternate group networks one by one, so as to obtain the point-related fault tolerance of the alternate group networks.
However, in actual use, some structures in the alternate group network often fail, so that considering the structure fault tolerance of the network has practical significance and value.
Disclosure of Invention
The application provides a method, a device, equipment and a storage medium for determining the fault tolerance of an alternate group network structure, which can determine the fault tolerance of the structure according to the dimension of the structure and improve the determination efficiency of the fault tolerance of the network structure. The application provides the following technical scheme:
in a first aspect, a method for determining fault tolerance of AN alternative group network structure is applied to AN alternative group network AN n In (2), the alternating groupsNetwork AN n Including n! (ii)/2 vertices, n ≧ 4, the method comprising:
determining an independent vertex in the alternate group network, wherein the independent vertex is any one vertex in the alternate group network;
determining a first set of neighbors of the independent vertex; the first neighbor set comprises n-1 vertices; the first neighbor set comprises a first vertex, a second vertex and n-3 third vertices;
determining a second neighbor set corresponding to the appointed vertex in the first neighbor set; the designated vertices include the first vertex and the third vertex;
for the designated vertex and a second neighbor set corresponding to the designated vertex, determining K of the designated vertex 1，t A structure set;
determining K of the alternate cluster network according to the size of the structure set 1，t -structural connectivity and a sub-structural connectivity upper bound;
using said K 1，t -structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
Optionally, the determining a second neighbor set corresponding to the specified vertex in the first neighbor set includes:
for alternate group network AN n Determine a first neighbor set v of u, let v ═ u i I is more than or equal to |2 and less than or equal to n }, then v includes the first vertex u 2 The second vertex u 3 And a third vertex u k (4≤k≤n)；
Determining the first vertex u 2 Second neighbor set of (u) { (u) 2 ) i |2≤i≤n，i≠3}；
Determining the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i |2≤i≤n，i≠k}。
Optionally, the determining, for the designated vertex and the second neighbor set corresponding to the designated vertex, the structure set of the designated vertex includes:
the first vertex u is 2 And said first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 |, form 1K 1，t Structure wherein t is less than or equal to n-2;
the third vertex u k (4. ltoreq. k. ltoreq.n) and the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to K } to form n-3 Ks 1，t Structure;
the 1K 1，t Structure and said n-3 Ks 1，t Storing the structure into a preset structure set to obtain a structure set of a first neighbor set containing the appointed vertex, wherein the structure set comprises n-2K 1，t And (5) structure.
Optionally, the determining K of the alternate group network according to the size of the structure set 1，t -a structural connectivity and a substructure connectivity upper bound comprising:
determining the size n-2 of the specified structure set as the K 1，t -structural connectivity and sub-structural connectivity upper bound.
Optionally, said first vertex u 2 And said first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 |, form 1K 1，t A structure, comprising:
the first vertex u is 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 is divided into neighbor vertexes (u) 2 ) 2 And set of neighbor vertices { (u) 2 ) i I is not less than 4 and not more than n, wherein the neighbor vertex (u) 2 ) 2 And said second vertex u 3 Likewise, the set of neighbor vertices { (u) 2 ) i I is more than or equal to |4 and less than or equal to n } comprises n-3 vertexes; from the set of neighbor vertices { (u) 2 ) i I is more than or equal to l 4 and less than or equal to n, determining any t-1 neighbor vertexes;
based on the neighbor vertex (u) 2 ) 2 And the t-1 neighbor vertices, with the first vertex u 2 Make up of the 1K 1，t And (5) structure.
Optionally, said associating said third vertex u k (4. ltoreq. k. ltoreq.n) andthe third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to K } to form n-3 Ks 1，t A structure, comprising:
from the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to l 2 and less than or equal to n, i is not equal to k, and arbitrary t neighbor vertexes are determined;
based on the t neighbor vertices, u k (K is more than or equal to 4 and less than or equal to n) constitutes the n-3 Ks 1，t And (5) structure.
Optionally, said using said K 1，t -a structural connectivity and sub-structural connectivity upper bound determines a structural fault tolerance of the alternate group network, comprising:
deleting the K in an alternate group network 1，t After the structure is gathered, whether the deleted alternate cluster networks are communicated or not is determined; under the condition that the alternate group network is not communicated, according to the K 1，t -structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
In a second aspect, AN apparatus for determining fault tolerance of AN alternative group network structure is provided, which is used in AN alternative group network, AN n Including n! The/2 vertexes, n is more than or equal to 4, and the device comprises:
a first determining module, configured to determine an independent vertex in the alternating group network, where the independent vertex is any vertex in the alternating group network;
a second determination module to determine a first neighbor set of the independent vertex; the first neighbor set comprises n-1 vertices; the first neighbor set comprises a first vertex, a second vertex and n-3 third vertices;
a third determining module, configured to determine a second neighbor set corresponding to the designated vertex in the first neighbor set; the designated vertices include the first vertex and the third vertex;
a fourth determining module, configured to determine, for the specified vertex and a second neighbor set corresponding to the specified vertex, a structure set of the specified vertex;
a fifth determining module, configured to determine K of the alternate group network according to a size of the structure set 1，t -structural connectivity and sub-structural connectivity upper bound;
a sixth determining module for using the K 1，t -structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
In a third aspect, an electronic device is provided, the device comprising a processor and a memory; the memory has stored therein a program that is loaded and executed by the processor to implement the alternating group network structure fault tolerance determination method provided by the first aspect.
In a fourth aspect, a computer-readable storage medium is provided, in which a program is stored, and the program is used for implementing the method for determining fault tolerance of an alternate group network structure provided in the first aspect when being executed by a processor.
The beneficial effects of this application include at least: by being based on K 1，t Determining K by the size of the structure set 1，t Upper bounds on connectivity and connectivity of substructures, using K 1，t And determining the structural fault tolerance of the alternate group network according to the structural connectivity and the upper bound of the substructure connectivity, so that the structural fault tolerance can be determined according to the dimension of the structure, and the determination efficiency of the structural fault tolerance is improved.
The foregoing description is only an overview of the technical solutions of the present application, and in order to make the technical solutions of the present application more clear and clear, and to implement the technical solutions according to the content of the description, the following detailed description is made with reference to the preferred embodiments of the present application and the accompanying drawings.
Drawings
FIG. 1 is a diagram illustrating relationships between neighbor vertices provided in an embodiment of the present application;
fig. 2 is a schematic structural diagram of an alternate group network corresponding to n-3 and 4 according to an embodiment of the present application;
FIG. 3 is a schematic diagram of a substructure cut of an alternate swarm network provided by one embodiment of the present application;
FIG. 4 is a schematic diagram of a substructure cut of another alternate swarm network provided by an embodiment of the present application;
FIG. 5 shows K provided in an embodiment of the present application 1，1 、K 1，2 、K 1，3 And K 1，t Schematic structural diagram of (a);
FIG. 6 is a flow chart of a method for determining fault tolerance of an alternate group network configuration according to an embodiment of the present application;
FIG. 7 is a diagram illustrating the neighbors of any vertex u and u in an alternate group network according to an embodiment of the present application;
FIG. 8 illustrates an independent vertex u and its neighbors u according to an embodiment of the present application 2 K of 1，t A schematic of the structure;
FIG. 9 illustrates an independent vertex u and its neighbors u according to an embodiment of the present application 5 K of 1，t A schematic of the structure;
FIG. 10 shows K for an independent vertex u and its neighbors, according to an embodiment of the present application 1，t A flow chart of the structure set;
fig. 11 is a block diagram of an embodiment of the present application providing n-4K 1，2 A schematic of a structure set;
fig. 12 is a block diagram of an embodiment of the present application providing n-4K 1，1 A schematic of a structure set;
FIG. 13 is a block diagram of a network fabric fault tolerance determination apparatus provided in one embodiment of the present application;
FIG. 14 is a block diagram of an electronic device provided by one embodiment of the application.
Detailed Description
The following detailed description of embodiments of the present application will be made with reference to the accompanying drawings and examples. The following examples are intended to illustrate the present application, but are not intended to limit the scope of the present application.
First, several terms referred to in the present application will be described.
Alternative group network AN n : with n! A/2 vertices, each labeled {1, 2, …, n } in an even arrangement. An arrangement with an even number of inversions is called an even arrangement. Any two digits in a permutation are said to be in reverse order if the large digit is preceding. Such as the light source 31245, for example,<3，1>，<3，2>is in reverse order, so 31245 is an even permutation. The two vertices x, y are labeled with the following condition, and referring to fig. 1 in particular, the two vertices x ═ a 1 a 2 a 3 ...a n ，y＝b 1 b 2 b 3 ...b n Connecting:
(1)a 1 ＝b 3 ，a 2 ＝b 1 ，a 3 ＝b 2 and a j ＝b j for 4≤j≤n。
(2)a 1 ＝b 2 ，a 2 ＝b 3 ，a 3 ＝b 1 and a j ＝b j for 4≤j≤n。
(3)a 1 ＝b 2 ，a 2 ＝b 1 ，a 3 ＝b 1 and a 3 ＝b i a i ＝b 3 ，a j ＝b j for{4≤j≤n}-{i}。
such as vertex 12345 being connected to vertex 32145 and vertex 12345 being connected to vertex 13245. With particular reference to fig. 2 and 3, n is 3,4 and 5.
Neighbor: two vertexes are connected, and then the two vertexes are adjacent to each other.
For AN n Any vertex u in (2) and the neighbor satisfying the above condition (1) is marked as u 2 . E.g., vertex u 1234, its neighbor 2314 is denoted as u 2 。
The neighbor satisfying the above condition (2) is denoted as u 3 E.g., vertex u-1234, its neighbor 3124 is denoted as u 3 。
The neighbors satisfying the above condition (3) are denoted as { u } i I is more than or equal to |4 and less than or equal to n }. E.g., vertex u 1234, its neighbor 21435 is denoted u 4 21543 is denoted as u 5 。
Each u has n-1 neighbors, denoted as { u i |2≤i≤n}，u i The j-th neighbor of (1), denoted as { (u) i ) j |2≤i，j≤n}。
Let u be a 1 a 2 a 3 ... a n Then u is 2 ＝a 2 a 3 a 1 ... a n ，u 3 ＝a 3 a 1 a 2 ... a n ，(u 2 ) 2 ＝a 3 a 1 a 2 ... a n ，(u 2 ) 3 ＝a 1 a 2 a 3 ... a n . Can see (u) 2 ) 2 ＝u 3 ，(u 2 ) 3 U. I.e. u 2 And u 3 Are directly connected. Vertices 2314 and 3124 are seen adjacent in fig. 2.
u k ＝a 2 a 1 a k ... a 3 ... a n (4≤k≤n)，(u k ) k ＝a 1 a 2 a 3 .. a k .... a n In what appears is (u) k ) k ＝u。
Sub graph cut (subgraph cut): let F ═ H 1 ，H 2 ，...，H t It is a set of sub-graphs of graph G, i.e. each element in F is a sub-graph of G. If V (F) is deleted so that G is not connected, F is called a sub-graph of graph G.
H-structural cut (H-structure cut): if each element in the subgraph cut F is isomorphic to H, then F is called an H-structure cut. Typically a graph has many H-structure cuts.
Such as: referring to fig. 3, the deletion of three triangle structures in the dashed box makes the graph unconnected, and the set of these triangle structures is a triangle-structure cut.
H-structural connectivity: the size of the structural cut with the least number of elements in the H-structural cut is the H-structural connectivity, denoted as κ (G; H).
H-substructure cut (H-substructure cut): if each element in the subgraph cut F is isomorphic to a connected subgraph of H, then F is called an H-substructure cut. Typically a graph has many H-substructural cuts.
Referring to fig. 4, the graph can be made unconnected by deleting three structures in the dashed box of the graph. Since all three structures are a subgraph of the square structure, the set of these structures is a square-substructure cut.
H-substructure connectivity: the size of the substructure cut with the least number of elements in the H-substructure cut is the H-substructure connectivity, denoted as κ s (G；H)。
The structure connectivity and the substructure connectivity can be used to measure the structure fault tolerance of the network. In particular, the reliability of the network is measured when some of the structures fail. The larger the structural connectivity and the substructure connectivity of the network is, the better the fault tolerance of the network is when a structural fault occurs in the network. Without loss of generality, kappa (G; H) is not less than kappa s (G；H)。
The main objectives of the present application are: giving the alternative group network AN for any integer n ≧ 4 n Above about K 1，t -an upper bound of structural connectivity and sub-structural connectivity. In particular, with AN alternative group network AN n To construct the desired structure set F, such that after v (F) is removed, the group network AN is alternated n And F is a structural section. According to the definition of structural connectivity, structural connectivity is the minimum of structural cuts that make the graph non-connected. The currently constructed structure set F is one of many that is likely to be the smallest, so the value of the structure connectivity must be less than or equal to | F |. The size of F is the alternative group network AN n K of 1，t -an upper bound of structural connectivity. At the same time, since kappa (AN) n ；H)≥κ s (AN n (ii) a H) Kappa can be obtained s (AN n ；H)≤|F|。
Wherein, K 1，t The shape of (2) is shown in fig. 5.
Fig. 6 is a flowchart of a method for determining fault tolerance of a network structure according to AN embodiment of the present application, which is applied to AN alternative group network AN n In alternative group network AN n Including n! The method at least comprises the following steps of,/2 vertexes, n is more than or equal to 4:
Wherein, the independent vertex is any one vertex in the alternate group network.
At step 602, a first set of neighbors to the independent vertex is determined.
Wherein the first neighbor set comprises n-1 vertices; the first neighbor set includes a first vertex, a second vertex, and a third vertex, the third vertex having n-3.
In this embodiment, the first vertex is a vertex that satisfies the relationship (1) with the independent vertex; the second vertex is a vertex satisfying the relationship (2) with the independent vertex; the third vertex is a vertex satisfying the above relationship (3) with the independent vertex.
As shown in FIG. 7, for AN alternate group network AN n Has n-1 neighbors { u } i I is more than or equal to |2 and less than or equal to n }. Wherein u is 2 And u 3 Adjacent to each other, and (u) 2 ) 2 ＝u 3 ，(u 2 ) 3 ＝u。
In the present embodiment, the designated vertices include a first vertex and a third vertex;
correspondingly, determining a second neighbor set to which the specified vertex in the first neighbor set corresponds includes determining a second neighbor set for the first vertex and a second neighbor set for a third vertex.
In particular, for AN alternate group network AN n Determining a first set of neighbors v of u, let v ═ u { (u) } for any independent vertex u in (c) i I is more than or equal to |2 and less than or equal to n }, then v includes the first vertex u 2 The second vertex u 3 And a third vertex u k (k is more than or equal to 4 and less than or equal to n); determining a first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, and i is not equal to 3 }; determining a third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i |2≤i≤n，i≠k}。
At the first vertex u 2 Includes a vertex (u) in the neighbor vertex 2 ) 3 And (u) 2 ) 3 U, i.e. vertex (u) 2 ) 3 Identical to the independent vertex u, and therefore the first vertex u is determined 2 The second neighbor set of (u), the vertex (u) needs to be replaced 2 ) 3 Removing; oppositely, at a third vertex u k (4. ltoreq. k. ltoreq.n) includes a vertex (u) in the neighbor vertices k ) k And (u) k ) k U, i.e. vertex (u) k ) k Identical to the independent vertex u, and therefore the third vertex u is determined k (4. ltoreq. k. ltoreq.n) of the second neighbor set, the vertex (u) needs to be replaced k ) k And (4) excluding.
In addition, the first vertex u 2 Includes a vertex (u) in the neighbor vertex 2 ) 2 And (u) 2 ) 2 ＝u 3 I.e. vertex (u) 2 ) 2 A second vertex u from the independent vertex u 3 Similarly, therefore, in this embodiment, the second vertex u does not need to be determined 3 The second set of neighbors.
Since the designated vertex includes the first vertex and the third vertex, K of the designated vertex 1，t K including a first vertex in a structural set 1，t K of structure and third vertex 1，t And (5) structure. Wherein t is less than or equal to n-2.
Specifically, for the designated vertex and the second neighbor set corresponding to the designated vertex, K of the designated vertex is determined 1，t A set of structures comprising: the first vertex u 2 And a first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 |, form 1K 1，t Structure (c); putting the third vertex u k (4. ltoreq. k. ltoreq.n) and a third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors ((u) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to K } to form n-3 Ks 1，t Structure; 1K 1，t Structure and n-3K 1，t The structure is stored in a preset structure set to obtain a structure set of appointed vertexes, and the structure set comprises n-2 Ks 1，t And (5) structure.
Wherein the first vertex u is divided into 2 And a first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 |, form 1K 1，t A structure, comprising: the first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 is divided into neighbor vertexes (u) 2 ) 2 And set of neighbor vertices { (u) 2 ) i I is more than or equal to |4 and less than or equal to n }, wherein the vertex (u) of the neighbor is 2 ) 2 And a second vertex u 3 Same, set of neighbor vertices { (u) 2 ) i I is more than or equal to |4 and less than or equal to n } comprises n-3 vertexes; from a set of neighbor vertices { (u) 2 ) i I is more than or equal to |4 and less than or equal to n } to determine any t-1 neighbor vertexes; based on neighbor vertices (u) 2 ) 2 And t-1 neighbor vertices, with the first vertex u 2 Make up of 1K 1，t And (5) structure.
Such as: as shown in FIG. 8, first find u 2 Except that u ═ u 2 ) 3 All neighbors except { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3}, and u is less than or equal to n 2 Neighbor set selection of (u) 2 ) 2 ＝u 3 And other arbitrary t-1 neighbors, plus u 2 Form a K 1，t And (5) structure. For example, suppose t is 4 except u 3 Besides, any 3 other neighbors are selected to form a K 1，4 And (5) structure.
Putting the third vertex u k (4. ltoreq. k. ltoreq.n) and a third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to K } to form n-3 Ks 1，t A structure, comprising: from the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to k, and arbitrary t neighbor vertexes are determined; based on t neighboring vertices, with a third vertex u k (K is more than or equal to 4 and less than or equal to n) constitutes n-3 Ks 1，t And (5) structure.
Such as: as shown in FIG. 9, find u k (4. ltoreq. k. ltoreq.n) except that u ═ u k ) k All neighbors except { (u) k ) i I is not less than 2 and not more than n, i is not equal to k) from u k Randomly selects t neighbors in the neighbor set, adds u k Form a K 1，t And (5) structure. For example, in u k U is selected from (k is more than or equal to 4 and less than or equal to n) 5 Assuming that t is 4, an arbitrary 4 u are selected 5 Neighbor of (c), plus u 5 Can form a K 1，4 And (5) structure.
K for determining independent vertex u as shown with reference to FIG. 10 1，t A flow chart of a structure set. For alternate group network AN n Any independent vertex u in the tree, and all the neighbors { u of u are obtained i I is more than or equal to |2 and less than or equal to n }, referring to FIG. 8, an independent vertex u has n-1 neighbors including u 2 、u 3 And u k (k is more than or equal to 4 and less than or equal to n); find u 2 All neighbors except u { (u) 2 ) i I is more than or equal to l 2 and less than or equal to n, and i is not equal to 3 }; from u 2 Is selected from the neighbor set (u) 2 ) 2 And other t-1 neighbors form K 1，t Putting the structure body into the set H; find u k All neighbors of (4 ≦ k ≦ n) except u { (u ≦ k ≦ n) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to k }; from u k (K is more than or equal to 4 and less than or equal to n) in the neighbor set, selecting t neighbors to form K 1，t Putting the structure body into the set H; the size of the set H is determined.
In summary, there are 1+ n-3 ═ n-2 Ks in the set H 1，t A structure. For alternate group network AN n First, a neighbor u of u is selected 2 Construct a K 1，t And (5) structure. And then for neighbor u k (k is not less than 4 and not more than n), and u is selected k Any t neighbors of (K) to form 1，t And (5) structure. So that in total n-2K components can be constructed 1，t Structure, since these structures cover all the neighbor nodes of u, AN after deleting these structures n Will not be connected, in which case u is an independent vertex. Thus, AN n K of 1，t The upper bound of structural connectivity and substructural connectivity is n-2, denoted κ (AN) n ；K 1，t ) N-2 and kappa s (AN n ；K 1，t ) N-2 is less than or equal to. Therefore, K for the alternate group network is determined based on the size of the fabric set 1，t -an upper bound of structural and sub-structural connectivity comprising: determining a size n-2 of the specified structure set as K 1，t -structural connectivity and sub-structural connectivity upper bound.
Referring to fig. 11, to alternate group network AN 4 When u is 1234 and t is 2, then K is 1，t Structural configuration of K 1，2 Structure set H is H { {2314,3124, 3241}, {2143, 4213, 1423} }, after v (H) is deleted, AN 4 There is no communication, where 1234 is AN independent vertex, so H is a structure cut of size 2, so AN can be obtained 4 K of 1，2 The upper bound of structural connectivity is 2, written as: kappa (AN) n ；K 1，2 )≤2。
Referring to fig. 12, to alternate group network AN 4 When u is 1234 and t is 1, then K is 1，t Structural configuration of K 1，1 Structure set H is H { {2314,3124}, {2143, 1423} }, and after v (H) is deleted, AN 4 There is no communication, where 1234 is AN independent vertex, so H is a structure cut of size 2, so AN can be obtained 4 K of 1，1 The upper bound of structural connectivity is 2, written as: kappa (AN) n ；K 1，2 )≤2。
The present example also provides the code of the structure connectivity () for obtaining the alternate group network AN n K of 1，t -an upper bound for structural and sub-structural connectivity, the code being as follows:
firstly, arbitrary integer n is more than or equal to 3, and AN alternative group network AN can be constructed n An upper bound of upper structure connectivity, n-2 Ks constructed around the u's neighbors by giving any one vertex u 1，t Structure of AN n Is not connected, thereby obtaining AN n K of 1，t -an upper bound of structural connectivity and sub-structural connectivity.
Such as: for a 4-dimensional alternate group network AN 4 Considering that the vertex u is 1234 and t is 1, the structure connectivity (u, 4, 1) may be calledConstructed K 1，1 Set of structures H { {2314,3124}, {2143, 1423} }, after H is deleted, AN 4 Is not connected, so κ (AN) 4 ；K 1，1 ) 2 or less and kappa s (AN 4 ；K 1，1 ) Less than or equal to 2; k that can be constructed by calling StructureConnectivity (u, 4, 2) considering vertex u-1234 and t-2 1，2 Set of structures H { {2314,3124, 3241}, {2143, 1423,4213} }, after H deletion, AN 4 Are not connected. So κ (AN) 4 ；K 1，2 ) 2 or less and kappa s (AN 4 ；K 1，2 )≤2。
Such as: for 5-dimensional alternate group network AN 5 K which can be constructed by calling StructureConnectivity (u, 5, 1) while considering that the vertex u is 12345 and t is 1 1，1 Set of structures H { {23145, 31245}, {21435, 14235}, {21543, 15243} }, after H deletion, AN 5 Is not connected, so κ (AN) 5 ；K 1，1 ) Less than or equal to 3 and kappa s (AN 5 ；K 1，1 ) Less than or equal to 3; k that can be constructed by calling structural connectivity (u, 5, 2) considering that vertex u is 12345 and t is 2 1，2 Set of structures H { {23145, 31245, 32415} {21435, 14235,42135 }, {21543, 15243, 52143} }, after H deletion, AN 5 Is not connected, so κ (AN) 5 ；K 1，2 ) Less than or equal to 3 and kappa s (AN 5 ；K 1，2 ) Less than or equal to 3; k which can be constructed by calling structural connectivity (u, 5, 3) in consideration of the vertex u being 12345 and t being 3 1，3 Set of structures H { {23145, 31245, 32415, 32541} {21435, 14235,42135, 12534}, {21543, 15243, 52143, 12453} }, after deletion of H, AN 5 Is not connected, so κ (AN) 5 ；K 1，3 ) Less than or equal to 3 and kappa s (AN 5 ；K 1，3 )≤3。
Step 606, use K 1，t -the structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
In particular, deleting K in an alternate group network 1，t In the case of structure sets, according to K 1，t -structural connectionAnd determining the structural fault tolerance of the alternate group network by the aid of the connectivity and the substructure connectivity upper bound.
Structural fault tolerance of network and K of network 1，t The structural connectivity (or substructural connectivity) is in a positive correlation, i.e., K 1，t The larger the connectivity of the structure (or the connectivity of the substructures), the higher the fault tolerance of the structure by the alternate group network, i.e. the higher the fault tolerance of the structure.
Such as: if the structural connectivity of network a is 2, the structural connectivity of b is 5. If only 2 structures in the network a fail, the network a is not connected; even if 4 structures of the network b fail, the network b can still be connected, and at the moment, the structural fault tolerance of the network a is lower than that of the network b.
In summary, the method for determining the fault tolerance of the network structure provided by this embodiment is based on K 1，t Structure set to determine K 1，t Upper bound of structural and substructure connectivity, using K 1，t And determining the structural fault tolerance of the alternate group network by the structural connectivity and the substructure connectivity upper bound, and determining the structural fault tolerance from the structural dimension to improve the determination efficiency of the structural fault tolerance.
Fig. 13 is a block diagram of an alternate group network structure fault tolerance determination apparatus according to an embodiment of the present application. The alternate group network includes n! The device at least comprises the following modules according to the following steps: a first determination module 1310, a second determination module 1320, a third determination module 1330, a fourth determination module 1340, a fifth determination module 1350, and a sixth determination module 1360.
A first determining module 1310, configured to determine an independent vertex in the alternating group network, where the independent vertex is any vertex in the alternating group network;
a second determining module 1320 for determining a first neighbor set of the independent vertex; the first neighbor set comprises n-1 vertexes; the first neighbor set comprises a first vertex, a second vertex and n-3 third vertices;
a third determining module 1330, configured to determine a second neighbor set corresponding to the specified vertex in the first neighbor set; the designated vertex comprises a first vertex and a third vertex;
a fourth determining module 1340, configured to determine, for the specified vertex and the second neighbor set corresponding to the specified vertex, a structure set of the specified vertex;
a fifth determining module 1350, configured to determine K of the alternate group network according to the size of the structure set 1，t -structural connectivity and a sub-structural connectivity upper bound;
a sixth determining module 1360 to use K 1，t -the structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
For relevant details reference is made to the above-described method embodiments.
It should be noted that: in the above embodiment, when determining the fault tolerance of the alternate group network structure, the device for determining the fault tolerance of the alternate group network structure is only illustrated by dividing the functional modules, and in practical applications, the functions may be distributed by different functional modules according to needs, that is, the internal structure of the device for determining the fault tolerance of the alternate group network structure is divided into different functional modules to complete all or part of the functions described above. In addition, the alternate group network structure fault tolerance determining apparatus and the alternate group network structure fault tolerance determining method provided in the above embodiments belong to the same concept, and specific implementation processes thereof are described in detail in the method embodiments and are not described herein again.
FIG. 14 is a block diagram of an electronic device provided by one embodiment of the application. The device comprises at least a processor 1401 and a memory 1402.
Processor 1401 may include one or more processing cores, such as: 4 core processors, 8 core processors, etc. The processor 1401 may be implemented in at least one hardware form of DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). Processor 1401 may also include a main processor and a coprocessor, where the main processor is a processor for Processing data in an awake state, and is also referred to as a Central Processing Unit (CPU); a coprocessor is a low power processor for processing data in a standby state. In some embodiments, the processor 1401 may be integrated with a GPU (Graphics Processing Unit), which is responsible for rendering and drawing content that the display screen needs to display. In some embodiments, processor 1401 may further include an AI (Artificial Intelligence) processor for processing computing operations related to machine learning.
Memory 1402 may include one or more computer-readable storage media, which may be non-transitory. Memory 1402 may also include high speed random access memory, as well as non-volatile memory, such as one or more magnetic disk storage devices, flash memory storage devices. In some embodiments, a non-transitory computer readable storage medium in memory 1402 is used to store at least one instruction for execution by processor 1401 to implement the alternating group network fabric fault tolerance determination methods provided by method embodiments herein.
In some embodiments, the electronic device may further include: a peripheral interface and at least one peripheral. The processor 1401, the memory 1402 and the peripheral interface may be connected by a bus or signal lines. Each peripheral may be connected to the peripheral interface via a bus, signal line, or circuit board. Illustratively, peripheral devices include, but are not limited to: radio frequency circuit, touch display screen, audio circuit, power supply, etc.
Of course, the electronic device may include fewer or more components, which is not limited by the embodiment.
Optionally, the present application further provides a computer-readable storage medium, in which a program is stored, and the program is loaded and executed by a processor to implement the method for determining fault tolerance of an alternate group network structure according to the above method embodiment.
Optionally, the present application further provides a computer product, which includes a computer-readable storage medium, in which a program is stored, and the program is loaded and executed by a processor to implement the method for determining fault tolerance of an alternate group network structure according to the above-mentioned method embodiment.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method for determining fault tolerance of alternative group network structure is characterized in that the method is applied to alternative group network AN n In (1), the alternative group network AN n Including n! (ii)/2 vertices, n ≧ 4, the method comprising:
determining an independent vertex in the alternate group network, wherein the independent vertex is any one vertex in the alternate group network;
determining a first set of neighbors of the independent vertex; the first neighbor set comprises n-1 vertices; the first neighbor set comprises a first vertex, a second vertex and n-3 third vertices;
determining a second neighbor set corresponding to the appointed vertex in the first neighbor set; the designated vertices include the first vertex and the third vertex;
for the designated vertex and a second neighbor set corresponding to the designated vertex, determining K of the designated vertex 1，t A structure set;
determining K of the alternate cluster network according to the size of the structure set 1，t -structural connectivity and a sub-structural connectivity upper bound;
using said K 1，t -structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
2. The method of claim 1, wherein determining a second neighbor set to which a specified vertex in the first neighbor set corresponds comprises:
for alternate group network AN n Determine a first neighbor set v of u, let v ═ u i I is more than or equal to |2 and less than or equal to n }, then v includes the first vertex u 2 The second vertex u 3 And a third vertex u k (4≤k≤n)；
Determining the first vertex u 2 Second neighbor set of (u) { (u) 2 ) i |2≤i≤n，i≠3}；
Determining the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i |2≤i≤n，i≠k}。
3. The method of claim 2, wherein determining the structural set of the specified vertex for the specified vertex and the second neighbor set to which the specified vertex corresponds comprises: the first vertex u is 2 And said first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 |, form 1K 1，t Structure wherein t is less than or equal to n-2;
the third vertex u k (4. ltoreq. k. ltoreq.n) and the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to |2 and less than or equal to n, i is not equal to K } to form n-3 Ks 1，t Structure;
the 1K 1，t Structure and said n-3 Ks 1，t Storing the structure into a preset structure set to obtain a structure set of a first neighbor set containing the appointed vertex, wherein the structure set comprises n-2K 1，t And (5) structure.
4. The method of claim 3, wherein the size of the set of structures is selected according to the size of the set of structuresDetermining said alternate group network
A structure connectivity and substructure connectivity upper bound comprising:
determining a size n-2 of the specified structure set as the
The structural connectivity and the substructure connectivity upper bound.
5. The method of claim 3, wherein said assigning said first vertex u 2 And said first vertex u 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 |, form 1K 1，t A structure, comprising:
the first vertex u is 2 Second neighbor set of (u) { (u) 2 ) i I is more than or equal to |2 and less than or equal to n, i is not equal to 3 is divided into neighbor vertexes (u) 2 ) 2 And set of neighbor vertices { (u) 2 ) i I is not less than 4 and not more than n, wherein the neighbor vertex (u) 2 ) 2 And said second vertex u 3 Likewise, the set of neighbor vertices { (u) 2 ) i I is more than or equal to |4 and less than or equal to n } comprises n-3 vertexes;
from the set of neighbor vertices { (u) 2 ) i I is more than or equal to |4 and less than or equal to n } to determine any t-1 neighbor vertexes;
based on the neighbor vertex (u) 2 ) 2 And the t-1 neighbor vertices, with the first vertex u 2 Make up of the 1K 1，t And (5) structure.
6. The method of claim 3, wherein said assigning said third vertex u k (4. ltoreq. k. ltoreq.n) and the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k ) i I is more than or equal to I and less than or equal to n, i is not equal to K, and n-3K are formed 1，t A structure, comprising:
from the third vertex u k (4. ltoreq. k. ltoreq.n) of a second set of neighbors { (u) k )i|2≤N is not more than i, i is not equal to k, and arbitrary t neighbor vertexes are determined;
based on the t neighbor vertices, with the third vertex u k (K is more than or equal to 4 and less than or equal to n) constitutes the n-3 Ks 1，t And (5) structure.
7. The method of claim 1, wherein said using said
Determining the structural fault tolerance of the alternate group network by the structural connectivity and the substructure connectivity upper bound, wherein the method comprises the following steps:
deleting the K in an alternate group network 1，t After the structure is gathered, whether the deleted alternate cluster networks are communicated or not is determined; in the case that the alternate group network is not connected, according to the
The structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
8. AN alternative group network structure fault tolerance determination device for use in AN alternative group network (AN) n Including n! 2 vertexes, n is more than or equal to 4, and is characterized in that,
a first determining module, configured to determine an independent vertex in the alternating group network, where the independent vertex is any one vertex in the alternating group network;
a second determination module to determine a first neighbor set of the independent vertex; the first neighbor set comprises n-1 vertices; the first neighbor set comprises a first vertex, a second vertex and n-3 third vertices;
a third determining module, configured to determine a second neighbor set corresponding to the designated vertex in the first neighbor set; the designated vertices include the first vertex and the third vertex;
a fourth determining module, configured to determine, for the specified vertex and a second neighbor set corresponding to the specified vertex, a structure set of the specified vertex;
a fifth determining module for determining the alternate group network according to the size of the structure set
A structural connectivity and a substructure connectivity upper bound;
a sixth determining module for using the
The structural connectivity and sub-structural connectivity upper bound determine the structural fault tolerance of the alternate group network.
9. An electronic device, characterized in that the device comprises a processor and a memory; the memory stores a program that is loaded and executed by the processor to implement the alternating group network architecture fault tolerance determination method according to any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that the storage medium has stored therein a program which, when being executed by a processor, is adapted to carry out the method for determining fault tolerance of an alternate group network architecture according to any one of claims 1 to 7.
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