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A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem

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Abstract

We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation; this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Harrelson Hall 235, Campus Box 8205, Raleigh, NC, 27695-8205

    Kartik Krishnan

  2. Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    John E. Mitchell

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  1. Kartik Krishnan
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  2. John E. Mitchell
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Correspondence to Kartik Krishnan.

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Research supported in part by NSF grant numbers CCR–9901822 and DMS–0317323.

Work done as part of the first authors Ph.D. dissertation at RPI.

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Krishnan, K., Mitchell, J.E. A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem. Comput Optim Applic 33, 51–71 (2006). https://doi.org/10.1007/s10589-005-5958-3

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  • DOI: https://doi.org/10.1007/s10589-005-5958-3

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