Journal of Digital Convergence (디지털융복합연구)

The Society of Digital Policy and Management (한국디지털정책학회)
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A Heuristic-Based Algorithm for Maximum k-Club Problem

MkCP (Maximum k-Club Problem)를 위한 휴리스틱 기반 알고리즘

  • Kim, SoJeong (Department of Applied Mathematics, Kongju National University) ;
  • Kim, ChanSoo (Department of Applied Mathematics, Kongju National University) ;
  • Han, KeunHee (Department of Applied Mathematics, Kongju National University)
  • Received : 2021.08.04
  • Accepted : 2021.10.20
  • Published : 2021.10.28
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Abstract

Given an undirected simple graph, k-club is one of the proposed structures to model social groups that exist in various types in Social Network Analysis (SNA). Maximum k-Club Problem (MkCP) is to find a k-club of maximum cardinality in a graph. This paper introduces a Genetic Algorithm called HGA+DROP which can be used to approximate maximum k-club in graphs. Our algorithm modifies the existing k-CLIQUE & DROP algorithm and utilizes Heuristic Genetic Algorithms (HGA) to obtain multiple k-clubs. We experiment on DIMACS graphs for k = 2, 3, 4 and 5 to compare the performance of the proposed algorithm with existing algorithms.

k-club은 소셜 네트워크 분석에서 다양한 형태의 소셜 그룹을 설명하기 위해 제안된 그래프 모델 중 하나로, 단순 그래프에서 부분 정점 집합 S 에 의한 유도 부분그래프(Induced subgraph)의 지름이 k보다 작거나 같은 경우 S 를 k-club이라 한다. 본 논문에서는 유전알고리즘을 이용하여 그래프에서 크기가 최대인 k-club을 찾는 문제인 MkCP(Maximum k-Club Problem)을 계산하는 HGA+DROP 알고리즘을 제안한다. 본 알고리즘은 k-club을 위한 휴리스틱 알고리즘 k-CLIQUE & DROP을 변형하고 휴리스틱 유전 알고리즘(HGA)을 사용해 한 번의 수행으로 복수개의 k-club을 구하였다. 기존 알고리즘의 결과와 비교하기 위해 DIMACS 그래프들에 대하여 k가 2, 3, 4 그리고 5일 때 MkCP를 계산하였다.

Keywords

Acknowledgement

This work was supported by Building Data for AI Learning(Video Narrative and Q&A Data) from National Information Society Agency(NIA).

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