计算机科学 ›› 2021, Vol. 48 ›› Issue (6A): 543-551.doi: 10.11896/jsjkx.201100167

• 交叉&应用 • 上一篇    下一篇

基于格思想的图结构相似问题的算法

王晓敏1,2, 苏静1,2, 姚兵3   

  1. 1 北京大学信息科学技术学院 北京100871
    2 北京大学高可信软件技术教育部重点实验室 北京100871
    3 西北师范大学数学与统计学院 兰州730070
  • 出版日期:2021-06-10 发布日期:2021-06-17
  • 通讯作者: 苏静(jingsu@pku.edu.cn)
  • 作者简介:wmxwm0616@163.com
  • 基金资助:
    国家自然科学基金重点研发计划(2019YFA0706401);国家自然科学基金重点项目(61632002);国家自然科学基金面上项目(61872166);国家自然科学基金青年项目(61902005,62002002);国家自然科学基金(61662066)

Algorithms Based on Lattice Thought for Graph Structure Similarity

WANG Xiao-min1,2, SU Jing1,2, YAO Bing3   

  1. 1 School of Electronic Engineering and Computer Science,Peking University,Beijing 100871,China
    2 Key Laboratory of High Confidence Software Technologies,Peking University,Beijing 100871,China
    3 College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China
  • Online:2021-06-10 Published:2021-06-17
  • About author:WANG Xiao-min,born in 1989,Ph.D student.Her main research interests include graph theory and complex networks.
    SU Jing,born in 1993,Ph.D.Her main research interests include graph theory and complex network.
  • Supported by:
    Major Research Plan of the National Natural Science Foundation of China(2019YFA0706401),Key Program of the National Natural Science Foundation of China(61632002),General Program of the National Natural Science Foundation of China(61872166),Young Scientists Fund of the National Natural Science Foundation of China(61902005,62002002) and National Natural Science Foundation of China(61662066).

摘要: 文中首先给出了顶点撕裂运算与顶点重合运算的定义,基于顶点撕裂连通度的定义证明了连通图的顶点撕裂连通度等价于连通图的连通度;给出了图的 W-相似的定义。其次,给出了图撕裂组以及同构子图相似的定义,介绍了一种特殊图撕裂组和特殊图撕裂组匹配方法。再次,讲述了有关图和图撕裂组的运算和算法,主要有确定图撕裂组的算法、图撕裂收缩算法、图的顶点扩展和收缩算法。然后,给出了图的同构子图相似的基本定理。最后,总结全文并提出了几个值得以后深入研究的问题。

关键词: 格, 连通度, 撕裂运算, 图结构相似

Abstract: This paper gives the definition of vertex-splitting operation and vertex-coinciding operation,introduces a new kind of connectivity-vertex-splitting connectivity based on the definition of vertex-splitting operations,proves that vertex-splitting connectivity is equivalent to connectivity of the connected graph,gives the definition of W-similarity.Secondly,it presents the definition of graph-splitting group and isomorphic subgraphs,and introduces a method for special graph-splitting group and special graph-splitting group matching.Again,it describes the operations and algorithms of graphs and graph-splitting groups,including,deterministic graph-splitting group algorithm,graph-splitting contracting algorithms,vertex expending and contracting algorithm of a graph.Then,it discusses the basic similarities of isomorphic subgraphs of graphs.Finally,it makes a brief conclusion and puts forward a few issues for further study.

Key words: Connectivity, Graph structure similarity, Lattice, Splitting operation

中图分类号: 

  • TP311
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