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The maximum ratio clique problem

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Abstract

This paper introduces a fractional version of the classical maximum weight clique problem, the maximum ratio clique problem, which is to find a maximal clique that has the largest ratio of benefit and cost weights associated with the clique’s vertices. NP-completeness of the decision version of the problem is established, and three solution methods are proposed. The results of numerical experiments with standard graph instances, as well as with real-life instances arising in finance and energy systems, are reported.

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Acknowledgments

This research was partially supported by the US Department of Energy Grant DE-SC0002051 and US Air Force Office of Scientific Research Award No. FA9550-12-1-0103. The authors gratefully acknowledge the comments by two referees.

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  1. Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, 77843-3131, USA

    Samyukta Sethuraman & Sergiy Butenko

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  1. Samyukta Sethuraman
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  2. Sergiy Butenko
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Correspondence to Samyukta Sethuraman.

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Sethuraman, S., Butenko, S. The maximum ratio clique problem. Comput Manag Sci 12, 197–218 (2015). https://doi.org/10.1007/s10287-013-0197-z

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