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Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations

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Abstract

Given a simple undirected graph, the problem of finding a maximum subset of vertices satisfying a nontrivial, interesting property Π that is hereditary on induced subgraphs, is known to be NP-hard. Many well-known graph properties meet the above conditions, making the problem widely applicable. This paper proposes a general purpose exact algorithmic framework to solve this problem and investigates key algorithm design and implementation issues that are helpful in tailoring the general framework for specific graph properties. The performance of the algorithms so derived for the maximum s-plex and the maximum s-defective clique problems, which arise in network-based data mining applications, is assessed through a computational study.

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Acknowledgements

We would like to thank the referees for providing useful suggestions, which helped us to significantly improve the paper. This research was supported in part by the US Department of Energy Grant DE-SC0002051 and the US Air Force Office of Scientific Research Grants FA9550-09-1-0154 and FA9550-12-1-0103.

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Authors and Affiliations

  1. Microsoft Corp., One Microsoft Way, Redmond, WA, 98052, USA

    Svyatoslav Trukhanov

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

    Chitra Balasubramaniam & Sergiy Butenko

  3. School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, 74078, USA

    Balabhaskar Balasundaram

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  1. Svyatoslav Trukhanov
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  2. Chitra Balasubramaniam
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  3. Balabhaskar Balasundaram
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  4. Sergiy Butenko
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Correspondence to Sergiy Butenko.

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Trukhanov, S., Balasubramaniam, C., Balasundaram, B. et al. Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations. Comput Optim Appl 56, 113–130 (2013). https://doi.org/10.1007/s10589-013-9548-5

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