Maximum cut‐clique problem: ILS heuristics and a data analysis application

Martins, Pedro; Ladrón de Guevara, Antonio; Ramalhinho-Lourenço, Helena

doi:http://dx.doi.org/10.1111/itor.12120

Maximum cut‐clique problem: ILS heuristics and a data analysis application

Citation

Martins P, Ladrón A, Ramalhinho H. Maximum cut-clique problem: ILS heuristics and a data analysis application. Int Trans Oper Res. 2014 Sep 5;22(5):775-809. DOI: 10.1111/itor.12120

Abstract

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.