Annals of Operations Research

, Volume 216, Issue 1, pp 145–161

A branch-and-bound approach for maximum quasi-cliques

  • Foad Mahdavi Pajouh
  • Zhuqi Miao
  • Balabhaskar Balasundaram
Article

DOI: 10.1007/s10479-012-1242-y

Cite this article as:
Mahdavi Pajouh, F., Miao, Z. & Balasundaram, B. Ann Oper Res (2014) 216: 145. doi:10.1007/s10479-012-1242-y

Abstract

Detecting quasi-cliques in graphs is a useful tool for detecting dense clusters in graph-based data mining. Particularly in large-scale data sets that are error-prone, cliques are overly restrictive and impractical. Quasi-clique detection has been accomplished using heuristic approaches in various applications of graph-based data mining in protein interaction networks, gene co-expression networks, and telecommunication networks. Quasi-cliques are not hereditary, in the sense that every subset of a quasi-clique need not be a quasi-clique. This lack of heredity introduces interesting challenges in the development of exact algorithms to detect maximum cardinality quasi-cliques. The only exact approaches for this problem are limited to two mixed integer programming formulations that were recently proposed in the literature. The main contribution of this article is a new combinatorial branch-and-bound algorithm for the maximum quasi-clique problem.

Keywords

Clique Quasi-clique Cluster detection Graph-based data mining 

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Foad Mahdavi Pajouh
    • 1
  • Zhuqi Miao
    • 1
  • Balabhaskar Balasundaram
    • 1
  1. 1.School of Industrial Engineering & ManagementOklahoma State UniversityStillwaterUSA