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Local-vertex-based spanning tree graph reconnection method

A technology for generating trees and vertices, applied in the field of mathematical graph theory, can solve problems such as irreducibility and structural variation

Inactive Publication Date: 2018-08-17
SHENZHEN WEITESHI TECH
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Problems solved by technology

[0004] To solve the problem of graph theory reconnection, the object of the present invention is to provide a spanning tree graph reconnection method based on local vertices. Firstly, a mechanism is defined to determine whether the spanning tree graph has isomorphic properties, so as to prevent the occurrence of Structural variation; then use the reconnection framework based on the Monte Carlo method to split and reconnect the head node and tail node of an edge connection, update its adjacent endpoints and nodes, and perform this process a limited number of times under certain conditions Iteration; for the graph generated by the reconnection framework, in order to cover the leak rate caused by randomness, it provides verification of ergodic properties, including irreducibility, aperiodicity and positive recursion

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[0031] It should be noted that, in the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

[0032] figure 1 It is a frame diagram of a spanning tree graph reconnection method based on local vertices in the present invention. It mainly includes isomorphism judgment function; reconnection framework; ergodic verification.

[0033] Isomorphism judgment function, given two graphs G 1 and G 2 , if there is a bijective function Θ:V(G 1 )→V(G 2 ) keeps the number of vertices and edges in the two graphs unchanged, namely:

[0034]

[0035] where {u,v} is the graph G 1 An edge of , Θ(u), Θ(v) is the graph G 2 The corresponding edge in

[0036] If all the edges in the two graphs satisfy the formula (1), the graph G can be judged 1 and G 2 is isomorphic, that is, the graph ...

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Abstract

The invention relates to a local-vertex-based spanning tree graph reconnection method. The method comprises steps of carrying out isomorphic function determination, carrying out frame reconnection, and carrying out ergodic verification. To be specific, a mechanism is defined to determine whether a spanning tree graph has an isomorphic nature, so that structural variation generation during the learning graph process is avoided; with a reconnection frame based on a Monte Carlo method, a head node and a tail node that are connected at an edge are split and reconnected, an adjacent end point and an adjacent node are updated, and iteration with the limited number of times is carried out on the process on a certain condition; and for the graph generated by the reconnection frame, ergodic property verification is provided to cover a leak rate caused by randomness, wherein the operation includes irreducibility, aperiodicity, and positive recursiveness. According to the invention, splitting andreconstruction are carried out by using the spanning tree graph based on the Monte Carlo method; a verification processed based on the Markov chain property is provided; and a spanning tree graph sampling method based on the fixed node number is led out creatively.

Description

technical field [0001] The invention relates to the field of mathematical graph theory, in particular to a method for reconnecting spanning tree graphs based on local vertices. Background technique [0002] Graph theory belongs to discrete mathematics in the discipline, so it has many characteristics of discrete mathematics. The emergence and development of many concepts and theories in graph theory are independent of each other, so they are divided into many independent topics. Its algorithm is a collection of a series of steps to solve problems, and is an important part of discrete mathematics. Graph theory has the characteristics of intuition, clarity, and simple problem solving. More importantly, many practical problems in practice can be divided into equivalent graph theory problems. Because of this, graph theory has wide application value: graph theory can describe various complex engineering systems and management problems with "graphs", and then use mathematical met...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06K9/62G06F17/15
CPCG06F17/15G06F18/2323G06F18/295
Inventor 夏春秋
Owner SHENZHEN WEITESHI TECH
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