Alternating group network dominating vertex determination method and device, equipment and storage medium
By recursively partitioning the alternating group network and randomly selecting dominant vertices to form a dominance set, the problems of resource allocation and load balancing in the alternating group network are solved, achieving resource optimization and system performance improvement.
Patent Information
- Application Number
- CN202411658626.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-20
- Publication Date
- 2026-05-22
AI Technical Summary
Currently, there is no effective algorithm to obtain the dominance set in alternating group networks, making resource allocation and load balancing difficult to achieve.
By recursively partitioning the alternating group network and randomly selecting dominant vertices to form a dominating set, all vertices are ensured to be adjacent to vertices in the dominating set, thus optimizing resource allocation and load balancing.
It achieves efficient resource allocation, reduces waste, improves system performance and stability, realizes load balancing, and improves overall system efficiency.
Smart Images
Figure CN122072659A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of computer network technology, and specifically relates to a method, apparatus, device and storage medium for determining the dominant vertex of an alternating group network. Background Technology
[0002] High-performance parallel computers (HPLC-PCs) are a reflection of a nation's comprehensive scientific and technological strength and a key technology supporting its sustained development. They play an increasingly important role in fields such as scientific research, education, petroleum, and meteorology. As the performance of HPLC-PCs continues to improve, the number of processors they possess becomes increasingly large. A network formed by connecting several processors in a specific way is called an interconnection network. An interconnection network can be represented by a simple graph G = (V, E), where V(G) represents the set of vertices and E(G) represents the set of edges. The vertices in graph G represent the processor nodes in the interconnection network, while the edges represent the connections between processor nodes.
[0003] Alternating Group Network AG n Alternating swarm networks are a typical interconnected network topology. They possess many superior properties, such as vertex transitivity, edge transitivity, strong hierarchy, high connectivity, small network diameter, and small average distance. Due to these advantages, alternating swarm networks have attracted increasing attention.
[0004] Given an undirected graph G = (V(G), E(G)), where V(G) is the set of vertices and E(G) is the set of edges, a subset S of V(G) is called the dominating set of G if and only if for any vertex v in V(G)-S, there exists some vertex u in S such that (u, v) ∈ E(G). A dominating set is a set of vertices in a graph G such that every vertex in G is either in the set or adjacent to a vertex in the set. In other words, the purpose of a dominating set is to "dominate" all other vertices in the graph through the vertices in the set.
[0005] like Figure 1 In G, S = {v4, v6} is a dominating set of G. For vertices v1, v2, v3, and v5, they are all adjacent to V6 in S, and vertex V7 is adjacent to v4 in S.
[0006] However, at present, no algorithm can obtain the dominance set in alternating group networks. Summary of the Invention
[0007] To address the aforementioned technical problems, this invention proposes a method, apparatus, device, and storage medium for determining the dominant vertices of an alternating group network.
[0008] To achieve the above objectives, the technical solution of the present invention is as follows:
[0009] In a first aspect, the present invention discloses a method for determining the dominant vertex of an alternating group network, comprising:
[0010] Step S1: Determine the n-dimensional alternating group network AG n All vertices of n ≥ 3;
[0011] Step S2: According to the vertex labeling rules, convert the n-dimensional alternating group network AG... n The process is recursively divided step by step until it is divided into several alternating group networks AG3;
[0012] Step S3: Randomly select a vertex from each alternating group network AG3. This vertex is the n-dimensional alternating group network AG. n The dominant vertex.
[0013] Based on the above technical solution, the following improvements can be made:
[0014] As a preferred option, the determination method also includes:
[0015] Step S4: Set all the dominating vertices randomly selected in step S3 to form the dominating set S.
[0016] As a preferred solution, the n-dimensional alternating group network AG n After removing the dominating vertices from the dominating set S, any remaining vertex can be adjacent to some dominating vertex in the dominating set S.
[0017] As a preferred embodiment, step S2 includes the following:
[0018] First, the n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n A n Let p1 be the set of all even permutations of <n>, and let each vertex be labeled with a number of length n: p1p2...p2p3 ... n For example, n≥3;
[0019] Secondly, according to the nth position of the vertex label p n AG n-dimensional alternating group network n Each vertex is assigned to an n alternating group network AG n-1 In the n alternating group network AG n-1 Each by It means, and The last digit of each vertex label is i, and 1 ≤ i ≤ n;
[0020] Then, according to the (n-1)th vertex label p n-1 Each n-1 dimensional alternating group network AG n-1 Each vertex is assigned to an n-1 alternating group network AG n-2 middle;
[0021] Repeat the above recursive steps until each vertex of each alternating group network AG4 is assigned to one of the four alternating group networks AG3, thus achieving partitioning.
[0022] Secondly, the present invention also discloses a device for determining the dominant vertices of an alternating group network, comprising:
[0023] The vertex determination module is used to determine the n-dimensional alternating group network AG. n All vertices of n ≥ 3;
[0024] The network partitioning module is used to partition the n-dimensional alternating group network AG according to the vertex labeling representation rules. n The process is recursively divided step by step until it is divided into several alternating group networks AG3;
[0025] The dominant vertex determination module is used to randomly select a vertex from each alternating group network AG3, and this vertex is the n-dimensional alternating group network AG3. n The dominant vertex.
[0026] As a preferred embodiment, the determining device further includes:
[0027] The dominance set forming module is used to collect all the dominance vertices randomly selected by the dominance vertex determination module to form a dominance set S.
[0028] As a preferred solution, the n-dimensional alternating group network AG n After removing the dominating vertices from the dominating set S, any remaining vertex can be adjacent to some dominating vertex in the dominating set S.
[0029] As a preferred approach, the network partitioning module is used to perform the following methods:
[0030] First, the n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n A n Let p1 be the set of all even permutations of <n>, and let each vertex be labeled with a number of length n: p1p2...p2p3 ... n For example, n≥3;
[0031] Secondly, according to the nth position of the vertex label p n AG n-dimensional alternating group network n Each vertex is assigned to an n alternating group network AGn-1 In the n alternating group network AG n-1 Each by It means, and The last digit of each vertex label is i, and 1 ≤ i ≤ n;
[0032] Then, according to the (n-1)th vertex label p n-1 Each n-1 dimensional alternating group network AG n-1 Each vertex is assigned to an n-1 alternating group network AG n-2 middle;
[0033] Repeat the above recursive steps until each vertex of each alternating group network AG4 is assigned to one of the four alternating group networks AG3, thus achieving partitioning.
[0034] Thirdly, the present invention also discloses a computing device, comprising:
[0035] One or more processors;
[0036] Memory;
[0037] And one or more programs, wherein the one or more programs are stored in memory and configured to be executed by one or more processors, and the one or more programs include instructions for determining the dominant vertices of any of the aforementioned alternating group networks.
[0038] Fourthly, the present invention also discloses a storage medium storing one or more computer-readable programs, the one or more programs including instructions adapted to be loaded by a memory and executed to determine any of the above-described methods for determining the dominant vertices of an alternating group network.
[0039] This invention discloses a method, apparatus, device, and storage medium for determining the dominant vertices of an alternating group network, which has the following beneficial effects:
[0040] First, this invention enables the acquisition of all dominating vertices in an alternating group network, forming a dominating set S, such that the n-dimensional alternating group network AG... n All remaining vertices in the set can be adjacent to some vertex in the dominating set S.
[0041] Second, when resources are limited, the dominance set of an interconnected network can optimize resource allocation, improve resource utilization, reduce resource waste, and enhance the overall performance of the system.
[0042] Third, in distributed systems, load balancing can be achieved through the dominant set of interconnected networks, thereby improving the overall efficiency and stability of the system. Attached Figure Description
[0043] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0044] Figure 1 This is a schematic diagram of the dominating set.
[0045] Figure 2 This is a schematic diagram of the vertex labels for the 3D alternating group network AG3.
[0046] Figure 3 This is a schematic diagram of vertex labeling for the 4-dimensional alternating group network AG4.
[0047] Figure 4 A flowchart illustrating a method for determining the dominant vertex of an alternating group network, as provided in an embodiment of the present invention.
[0048] Figure 5 A schematic diagram of five AG4s provided in an embodiment of the present invention;
[0049] (a) is A schematic diagram;
[0050] (b) is A schematic diagram;
[0051] (c) is A schematic diagram;
[0052] (d) is A schematic diagram;
[0053] (e) is A schematic diagram.
[0054] Figure 6 This is a schematic diagram of a device for determining the dominant vertices of an alternating group network, provided in an embodiment of the present invention.
[0055] Figure 7 This is a schematic diagram of a computing device provided in an embodiment of the present invention.
[0056] Among them: 201-point determination module, 202-network partitioning module, 203-vertex assignment determination module, 204-dominant set formation module;
[0057] 301 - Processor, 302 - Memory 302. Detailed Implementation
[0058] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0060] The expression “includes” is an “open-ended” expression, which means that there is a corresponding component or step, and should not be interpreted as excluding additional components or steps.
[0061] The following is a brief description of some of the technical terms or basic knowledge involved in this invention.
[0062] remember <n>Let be a set {1, 2, ..., n}, and n ≥ 3.
[0063] Let p = p1p2...p n p is a permutation on <n>, that is, for any integer i ≠ j, p i ∈<n> and p i ≠p i .
[0064] For integers 1 ≤ i ≤ n, p i Let p represent the i-th element in the permutation. If i > j, then p i <p j Then the element pair (p) is called an element pair. i <p j Let p be an inversion of p. If a permutation has an even number of inversions, it is called an even permutation.
[0065] Taking p = 13425 as an example, the element pairs (3, 2) and (4, 2) are two inversions, so p is an even permutation.
[0066] Let A be the name of the person in question. n for <n>The set of all even permutations of the integers, for any integer 3 ≤ i ≤ n. and For defined in A n The two operations on. (or The expression represents the permutation obtained by rotating the 1st, 2nd, and ith elements of p by one position clockwise (or counterclockwise).
[0067] For example, suppose p = 13425, then n-dimensional alternating group network AG n Each vertex is labeled with a length of n: p1p2...p n To express.
[0068] n-dimensional alternating group network AG n It is a typical interconnected network topology.
[0069] For any integer n ≥ 3, an n-dimensional alternating group network AG n It is recursively defined as follows:
[0070] (1) As Figure 2 As shown, AG3 is a graph consisting of three vertices labeled 123, 231 and 312, which are connected by three edges: (123, 312), (123, 231) and (231, 312).
[0071] (2) For any integer n≥4, AG n Composed of n AGs n-1 The copy constructor. For any integer 1 ≤ i ≤ n, let AG n The i-th subgraph, then The last digit of each vertex label is i.
[0072] AG n It can be divided into n copies: n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n Two vertices p, q∈A n Adjacent if and only if (abbreviated as) )or (abbreviated as) ), where i∈{3,4,...,n}.
[0073] Taking the 4-dimensional alternating group network AG4 as an example, its vertex labels are as follows: Figure 3 As shown.
[0074] To achieve the objectives of this invention, some embodiments of a method, apparatus, device, and storage medium for determining the dominant vertices of an alternating group network are provided, such as... Figure 4 As shown, the method for determining the dominant vertices in an alternating group network includes the following steps:
[0075] Step S101: Determine the n-dimensional alternating group network AG n All vertices of n ≥ 3;
[0076] Step S102: According to the vertex labeling rules, convert the n-dimensional alternating group network AG... n The process is recursively divided step by step until it is divided into several alternating group networks AG3;
[0077] Step S103: Randomly select a vertex from each alternating group network AG3. This vertex is the n-dimensional alternating group network AG. n The dominant vertex;
[0078] Step S104: Set all the dominating vertices randomly selected in step S103 to form the dominating set S.
[0079] This invention utilizes the characteristics of alternating group network structure to construct a dominant set S and an n-dimensional alternating group network AG. n After removing the dominating nodes in the dominating set S, any remaining vertex can be adjacent to a dominating vertex in the dominating set S.
[0080] Specifically, the characteristics of alternating group network structures are described below.
[0081] An n-dimensional alternating group network AG n Composed of n AGs n-1 Copy (i.e.: It is constructed from ) wherein: each AG n-1 The last bit of each vertex label, i.e., the nth bit, is the same.
[0082] Each AG n-1 Composed of n-1 AGs n-2 Copy (i.e.: It is constructed from ) wherein: each AG n-2 The (n-1)th bit of each vertex label is the same.
[0083] Based on this characteristic, the same principle applies.
[0084] Until each AG4 is copied by 4 AG3 (i.e.: It is constructed from AG3, and the fourth bit of the label of each vertex of each AG3 is the same.
[0085] Based on the characteristics of the aforementioned alternating group network structure, this invention employs a stepwise recursive approach to transform an n-dimensional alternating group network AG... n It is gradually decomposed into many 3-dimensional alternating group networks AG3.
[0086] First, consider an n-dimensional alternating group network AG. n Decompose into n AGs n-1 ;
[0087] Then, each n-1 dimensional alternating group network AG n-1 Decompose into n-1 AGs n-2 ;
[0088] Finally, continue in this manner until each 4-dimensional alternating group network AG4 is decomposed into 4 AG3s.
[0089] Since each 3D alternating group network AG3 is a triangle, if we take any vertex s, the remaining two vertices are connected to s. Therefore, for each AG3, we randomly select a vertex within AG3, and this vertex is the dominating vertex. We then set all the dominating vertices together to form the dominating set S.
[0090] The dominance set S obtained through the above operations guarantees that V(AG) n For any point v in S, there is some point u in S that is adjacent to it.
[0091] Therefore, step S102 of the present invention includes the following:
[0092] First, the n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n A n Let p1 be the set of all even permutations of <n>, and let each vertex be labeled with a number of length n: p1p2...p2p3 ... n For example, n≥3;
[0093] Secondly, according to the nth position of the vertex label p n (i.e., the last one), the n-dimensional alternating group network AG n Each vertex is assigned to an n alternating group network AG n-1 In the n alternating group network AG n-1 Each by It means, and The last digit of each vertex label is i, and 1 ≤ i ≤ n;
[0094] Then, according to the (n-1)th vertex label p n-1 Each n-1 dimensional alternating group network AG n-1 Each vertex is assigned to an n-1 alternating group network AG n-2 In the n-1 alternating group network AG n-2 Each by It means, and The last digit of each vertex label is i, and 1≤i≤n-1;
[0095] Repeat the above recursive steps until each vertex of each alternating group network AG4 is assigned to one of the four alternating group networks AG3, thus achieving partitioning.
[0096] Take the 5-dimensional alternating group network AG5 as an example.
[0097] First, the 5-dimensional alternating group network AG5 is divided into 5 AG4s (i.e.: ),like Figure 5 As shown in (a), (b), (c), (d), and (e).
[0098] Then, each 4-dimensional alternating group network AG4 is divided into 4 AG3s.
[0099] Finally, a vertex is randomly selected from each 3D alternating group network AG3, which is the dominant vertex.
[0100] All dominating vertices form the dominating set S. Figure 5 The blue dots in (a) are randomly selected dots.
[0101] This example also provides code for generateSet() to obtain the dominator set S, as shown below:
[0102]
[0103]
[0104]
[0105] In some embodiments, for the 3D bubble sort star map alternating group network AG3, calling generateSet(3) yields the following result: the dominance set of AG3 is:
[123] .
[0106] For the 4-dimensional bubble sorting star map alternating group network AG4, calling generateSet(4) yields the following result: the dominance set of AG4 is [3241, 3412, 1423, 2314].
[0107] For the 5-dimensional bubble sorting star map alternating group network AG5, calling generateSet(5) yields the following result: the dominance set of AG5 is: [35421, 45231, 32541, 42351, 53412, 54132, 51342, 31452, 54213, 51423, 21543, 12453, 35214, 31524, 25134, 13254, 43215, 41325, 14235, 12345].
[0108] This invention can accurately determine the dominant vertices of an alternating group network, obtain the dominant set, and apply it to an interconnected network to achieve resource optimization, load balancing, and other functions.
[0109] Specifically, when resources are limited, resource allocation is optimized through the dominance set of the interconnected network. The system can rationally allocate resources based on the resource requirements of the dominating vertices in the dominance set, ensuring that critical nodes (i.e., the dominating vertices in the dominance set) or tasks receive sufficient resource support. This optimized allocation can improve resource utilization, reduce resource waste, and enhance the overall performance of the system.
[0110] In distributed systems, load balancing is achieved through the dominance set of an interconnected network. The system dynamically adjusts resource allocation based on the load of the dominating vertices in the dominance set to ensure load balance across all nodes (i.e., vertices). This helps avoid situations where some nodes are overloaded while others are idle, thereby improving the overall efficiency and stability of the system.
[0111] Furthermore, in some other embodiments, such as Figure 6 As shown, the present invention also discloses a device for determining the dominant vertex of an alternating group network, comprising:
[0112] Vertex determination module 201 is used to determine the n-dimensional alternating group network AG. n All vertices of n ≥ 3;
[0113] Network partitioning module 202 is used to partition the n-dimensional alternating group network AG according to the vertex labeling representation rules. n The process is recursively divided step by step until it is divided into several alternating group networks AG3;
[0114] Dominant vertex determination module 203 is used to randomly select a vertex from each alternating group network AG3, and this vertex is the n-dimensional alternating group network AG3. n The dominant vertex.
[0115] Furthermore, the determining device also includes:
[0116] The dominance set forming module 204 is used to set all the dominance vertices randomly selected by the dominance vertex determination module to form a dominance set S.
[0117] Furthermore, n-dimensional alternating group network AG n After removing the dominating vertices from the dominating set S, any remaining vertex can be adjacent to some dominating vertex in the dominating set S.
[0118] Furthermore, the network partitioning module is used to perform the following methods:
[0119] First, the n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n A n Let p1 be the set of all even permutations of <n>, and let each vertex be labeled with a number of length n: p1p2...p2p3 ... n For example, n≥3;
[0120] Secondly, according to the nth position of the vertex label p n AG n-dimensional alternating group network n Each vertex is assigned to an n alternating group network AG n-1 In the n alternating group network AG n-1 Each by It means, and The last digit of each vertex label is i, and 1 ≤ i ≤ n;
[0121] Then, according to the (n-1)th vertex label p n-1 Each n-1 dimensional alternating group network AG n-1 Each vertex is assigned to an n-1 alternating group network AG n-2 middle;
[0122] Repeat the above recursive steps until each vertex of each alternating group network AG4 is assigned to one of the four alternating group networks AG3, thus achieving partitioning.
[0123] Furthermore, it should be noted that the device for determining the dominant vertex of an alternating group network provided in the above embodiments is only illustrated by the division of the above functional modules when determining the dominant vertex. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device for determining the dominant vertex of an alternating group network can be divided into different functional modules to complete all or part of the functions described above.
[0124] Furthermore, the embodiments of the apparatus for determining the dominant vertex of an alternating group network and the method for determining the dominant vertex of an alternating group network provided in the above embodiments belong to the same concept, and their specific implementation process can be found in the method embodiments, which will not be repeated here.
[0125] Furthermore, in some other embodiments, such as Figure 7 As shown, the present invention also discloses a computing device, comprising:
[0126] One or more processors 301;
[0127] Memory 302;
[0128] And one or more programs, wherein the one or more programs are stored in memory 302 and configured to be executed by one or more processors 301, the one or more programs including instructions for the method of determining the dominant vertices of the alternating group network disclosed in the above embodiments.
[0129] Processor 301 may include one or more processing cores, such as a quad-core processor or an octa-core processor. Processor 301 may be implemented using at least one hardware form selected from DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and PLA (Programmable Logic Array). Processor 301 may also include a main processor and a coprocessor. The main processor, also known as a CPU (Central Processing Unit), is used to process data in the wake-up state; the coprocessor is a low-power processor used to process data in the standby state. In some embodiments, processor 301 may integrate a GPU (Graphics Processing Unit), which is responsible for rendering and drawing the content to be displayed on the screen. In some embodiments, processor 301 may also include an AI (Artificial Intelligence) processor, which is used to handle computational operations related to machine learning.
[0130] Memory 302 may include one or more computer-readable storage media, which may be non-transitory. Memory 302 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices or flash memory devices. In some embodiments, the non-transitory computer-readable storage media in memory 302 is used to store at least one instruction, which is executed by processor 301 to implement the method for determining the dominant vertices of an alternating group network provided in the method embodiments of the present invention.
[0131] In addition, the computing device may optionally include: a peripheral device interface and at least one peripheral device. The processor 301, memory 302, and peripheral device interface can be connected via a bus or signal lines. Each peripheral device can be connected to the peripheral device interface via a bus, signal lines, or a circuit board. Illustratively, peripheral devices include, but are not limited to: radio frequency circuitry, a touchscreen display, audio circuitry, and a power supply.
[0132] Of course, the computing device may also include fewer or more components, and this embodiment does not limit this.
[0133] Furthermore, in other embodiments, the present invention also discloses a storage medium storing one or more computer-readable programs, the one or more programs including instructions adapted to be loaded by memory and executed by the method for determining the dominant vertices of an alternating group network disclosed in the above embodiments.
[0134] This invention discloses a method, apparatus, device, and storage medium for determining the dominant vertices of an alternating group network, which has the following beneficial effects:
[0135] First, this invention enables the acquisition of all dominating vertices in an alternating group network, forming a dominating set S, such that the n-dimensional alternating group network AG... n All remaining vertices in the set can be adjacent to some vertex in the dominating set S.
[0136] Second, when resources are limited, the dominance set of an interconnected network can optimize resource allocation, improve resource utilization, reduce resource waste, and enhance the overall performance of the system.
[0137] Third, in distributed systems, load balancing can be achieved through the dominant set of interconnected networks, thereby improving the overall efficiency and stability of the system.
[0138] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the present invention. Various changes and modifications can be made to the present invention without departing from its spirit and scope. All such changes and modifications fall within the scope of the present invention as claimed, which is defined by the appended claims and their equivalents.< / n> < / n>
Claims
1. A method for determining the dominant vertices in an alternating group network, characterized in that, include: Step S1: Determine the n-dimensional alternating group network AG n All vertices of n ≥ 3; Step S2: According to the vertex labeling rules, convert the n-dimensional alternating group network AG... n The process is recursively divided step by step until it is divided into several alternating group networks AG3; Step S3: Randomly select a vertex from each alternating group network AG3. This vertex is the n-dimensional alternating group network AG. n The dominant vertex.
2. The determination method according to claim 1, characterized in that, The determination method further includes: Step S4: Set all the dominating vertices randomly selected in step S3 to form the dominating set S.
3. The determination method according to claim 2, characterized in that, n-dimensional alternating group network AG n After removing the dominating vertices from the dominating set S, any remaining vertex can be adjacent to some dominating vertex in the dominating set S.
4. The determining method according to any one of claims 1-3, characterized in that, Step S2 includes the following: First, the n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n A n Let p1 be the set of all even permutations of <n>, and let each vertex be labeled with a number of length n: p1p2...p2p3 ... n For example, n≥3; Secondly, according to the nth position of the vertex label p n AG n-dimensional alternating group network n Each vertex is assigned to an n alternating group network AG n-1 In the n alternating group network AG n-1 respectively by It means, and The last digit of each vertex label is i, and 1 ≤ i ≤ n; Then, according to the (n-1)th vertex label p n-1 Each n-1 dimensional alternating group network AG n-1 Each vertex is assigned to an n-1 alternating group network AG n-2 middle; Repeat the above recursive steps until each vertex of each alternating group network AG4 is assigned to one of the four alternating group networks AG3, thus achieving partitioning.
5. A device for determining the dominant vertices of an alternating group network, characterized in that, include: The vertex determination module is used to determine the n-dimensional alternating group network AG. n All vertices of n ≥ 3; The network partitioning module is used to partition the n-dimensional alternating group network AG according to the vertex labeling representation rules. n The process is recursively divided step by step until it is divided into several alternating group networks AG3; The dominant vertex determination module is used to randomly select a vertex from each alternating group network AG3, and this vertex is the n-dimensional alternating group network AG3. n The dominant vertex.
6. The determining device according to claim 5, characterized in that, The determining device further includes: The dominance set forming module is used to collect all the dominance vertices randomly selected by the dominance vertex determination module to form a dominance set S.
7. The determining device according to claim 6, characterized in that, n-dimensional alternating group network AG n After removing the dominating vertices from the dominating set S, any remaining vertex can be adjacent to some dominating vertex in the dominating set S.
8. The determining device according to any one of claims 5-7, characterized in that, The network partitioning module is used to perform the following methods: First, the n-dimensional alternating group network AG n Vertex set V(AG) n ) = A n A n Let p1 be the set of all even permutations of <n>, and let each vertex be labeled with a number of length n: p1p2...p2p3 ... n For example, n≥3; Secondly, according to the nth position of the vertex label p n AG n-dimensional alternating group network n Each vertex is assigned to an n alternating group network AG n-1 In the n alternating group network AG n-1 respectively by It means, and The last digit of each vertex label is i, and 1 ≤ i ≤ n; Then, according to the (n-1)th vertex label p n-1 Each n-1 dimensional alternating group network AG n-1 Each vertex is assigned to an n-1 alternating group network AG n-2 middle; Repeat the above recursive steps until each vertex of each alternating group network AG4 is assigned to one of the four alternating group networks AG3, thus achieving partitioning.
9. A computing device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by one or more processors, and the one or more programs include instructions for the method of determining the dominant vertices of an alternating group network as described in any of claims 1-4.
10. A storage medium, characterized in that, The storage medium stores one or more computer-readable programs, the programs including instructions adapted to be loaded by memory and executed as described in any of claims 1-4 for determining the dominant vertices of an alternating group network.