Annals of Operations Research

, Volume 262, Issue 1, pp 109–132 | Cite as

Detecting robust cliques in graphs subject to uncertain edge failures

  • Oleksandra Yezerska
  • Sergiy ButenkoEmail author
  • Vladimir L. Boginski
S.I.: Risk Management Approaches in Engineering Applications


This paper develops and compares several heuristic approaches, as well as an exact combinatorial branch-and-bound algorithm, for detecting maximum robust cliques in graphs subjected to multiple uncertain edge failures. The desired robustness properties are enforced using conditional value-at-risk measure. The proposed heuristics are adaptations of the well-known tabu search and GRASP methods, whereas the exact approach is an extension of Östergård’s algorithm for the maximum clique problem. The results of computational experiments on DIMACS graph instances are reported.


Maximum clique Robust clique Conditional value-at-risk Heuristic  Tabu search GRASP 



The authors would like to thank two anonymous referees whose suggestions helped to improve the paper. This material is based upon work supported by the AFRL Mathematical Modeling and Optimization Institute. Partial support by AFOSR under Grants FA9550-12-1-0103 and FA8651-12-2-0011, as well as the U.S. Department of Energy grant DE-SC0002051 is also gratefully acknowledged.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Oleksandra Yezerska
    • 1
  • Sergiy Butenko
    • 1
    Email author
  • Vladimir L. Boginski
    • 2
    • 3
  1. 1.Industrial and Systems EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of Industrial and Systems Engineering, Research and Engineering Education Facility (REEF)University of FloridaShalimarUSA
  3. 3.Department of Industrial Engineering and Management SystemsUniversity of Central FloridaOrlandoUSA

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