Annals of Operations Research

, Volume 216, Issue 1, pp 145–161 | Cite as

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

  • Foad Mahdavi Pajouh
  • Zhuqi Miao
  • Balabhaskar Balasundaram


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.


Clique Quasi-clique Cluster detection Graph-based data mining 


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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

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