Finding a maximum k-club using the k-clique formulation and canonical hypercube cuts

Original Paper

DOI: 10.1007/s11590-015-0971-7

Cite this article as:
Moradi, E. & Balasundaram, B. Optim Lett (2015). doi:10.1007/s11590-015-0971-7


Detecting low-diameter clusters is an important graph-based data mining technique used in social network analysis, bioinformatics and text-mining. Low pairwise distances within a cluster can facilitate fast communication or good reachability between vertices in the cluster. Formally, a subset of vertices that induce a subgraph of diameter at most k is called a k-club. For low values of the parameter k, this model offers a graph-theoretic relaxation of the clique model that formalizes the notion of a low-diameter cluster. Using a combination of graph decomposition and model decomposition techniques, we demonstrate how the fundamental optimization problem of finding a maximum size k-club can be solved optimally on large-scale benchmark instances that are available in the public domain. Our approach circumvents the use of complicated formulations of the maximum k-club problem in favor of a simple relaxation based on necessary conditions, combined with canonical hypercube cuts introduced by Balas and Jeroslow.


k-club Clique Low-diameter clusters Lazy cuts 

Funding information

Funder NameGrant NumberFunding Note
Air Force Office of Scientific Research
  • FA9550-12-1-0103
National Science Foundation
  • CMMI-1404971

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Industrial Engineering and ManagementOklahoma State UniversityStillwaterUSA

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