Annals of Operations Research

, Volume 249, Issue 1–2, pp 17–37 | Cite as

On robust clusters of minimum cardinality in networks



This paper studies two clique relaxation models, k-blocks and k-robust 2-clubs, used to describe structurally cohesive clusters with good robustness and reachability properties. The minimization version of the two problems are shown to be hard to approximate for \(k \ge 3\) and \(k \ge 4\), respectively. Integer programming formulations are proposed and a polyhedral study is presented. The results of sample numerical experiments on several graph instances are also reported.


Clique relaxations Connectivity k-Block k-Robust s-club  Structural cohesion 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringTexas A&M UniversityCollege StationUSA

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