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Maximum cut‐clique problem: ILS heuristics and a data analysis application
Author(s) -
Martins Pedro,
Ladrón Antonio,
Ramalhinho Helena
Publication year - 2015
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12120
Subject(s) - clique problem , clique , heuristics , clique sum , mathematics , iterated function , clique graph , clique percolation method , split graph , combinatorics , induced subgraph isomorphism problem , graph , computer science , mathematical optimization , chordal graph , line graph , complex network , mathematical analysis , 1 planar graph , voltage graph
This paper focuses on iterated local search heuristics for the maximum cut‐clique (MCC, or clique neighborhood) problem. Given an undirected graph G = ( V , E ) and a clique C of G , the cut‐clique is the set of edges running between C and V \ C , establishing the cut ( C , V \ C ). The MCC in G is to find a clique with the largest number of edges in the neighborhood of the clique, also known as the maximum edge‐neighborhood clique. This problem has been recently introduced in the literature together with a number of applications, namely, in cell biology instances. However, it has only been addressed so far by exact methods.In this paper, we introduce the first approximate algorithms for tackling the MCC problem, compare the results with the exact methodologies, and explore a new application within marketing analysis, which provide a new alternative perspective for mining market basket problems.