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On semidefinite programming relaxations of maximum \(k\)-section

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Abstract

We derive a new semidefinite programming bound for the maximum \(k\)-section problem. For \(k=2\) (i.e. for maximum bisection), the new bound is at least as strong as a well-known bound by Poljak and Rendl (SIAM J Optim 5(3):467–487, 1995). For \(k \ge 3\) the new bound dominates a bound of Karisch and Rendl (Topics in semidefinite and interior-point methods, 1998). The new bound is derived from a recent semidefinite programming bound by De Klerk and Sotirov for the more general quadratic assignment problem, but only requires the solution of a much smaller semidefinite program.

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Acknowledgments

The authors would like to thank Edwin van Dam, Willem Haemers, and René Peters for useful discussions on strongly regular graphs, and for providing several maximum-\(k\)-section instances on these graphs.

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Authors and Affiliations

  1. Department of Econometrics and OR, Tilburg University, Warandelaan 2, 5000 LE, Tilburg, The Netherlands

    Etienne de Klerk, Renata Sotirov & Cristian Dobre

  2. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Dmitrii Pasechnik

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  1. Etienne de Klerk
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  2. Dmitrii Pasechnik
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  3. Renata Sotirov
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  4. Cristian Dobre
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Correspondence to Etienne de Klerk.

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de Klerk, E., Pasechnik, D., Sotirov, R. et al. On semidefinite programming relaxations of maximum \(k\)-section. Math. Program. 136, 253–278 (2012). https://doi.org/10.1007/s10107-012-0603-2

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  • DOI: https://doi.org/10.1007/s10107-012-0603-2

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