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Polyhedral Computations for the Simple Graph Partitioning Problem

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    Abstract

    The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each containing no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we present a branch-and-cut algorithm for the problem that uses several classes of facet-defining inequalities as cuttingplanes. These are b-tree, clique, cycle with ear, multistar, and S, Tinequalities. Descriptions of the separation procedures that are used for these inequality classes are also given. In order to evaluate the usefulness of the inequalities and the overall performance of the branch-and-cut algorithm several computational experiments are conducted. We present some of the results of these experiments.

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    Bibliographic Info

    Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series CORAL Working Papers with number L-2005-02.

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    Length: 22 pages
    Date of creation: 03 Nov 2005
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    Handle: RePEc:hhb:aarbls:2005-002

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    Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
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    Keywords: Branch-and-cut algorithm; Facets; Graph partitioning; Multicuts; Separation procedures;

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    1. Macambira, Elder Magalhaes & de Souza, Cid Carvalho, 2000. "The edge-weighted clique problem: Valid inequalities, facets and polyhedral computations," European Journal of Operational Research, Elsevier, vol. 123(2), pages 346-371, June.
    2. Sørensen, Michael M., 2000. "Facet Defining Inequalities for the Simple Graph Partitioning Polytope," Working Papers 00-3, University of Aarhus, Aarhus School of Business, Department of Management Science and Logistics.
    3. Sorensen, Michael M., 2004. "New facets and a branch-and-cut algorithm for the weighted clique problem," European Journal of Operational Research, Elsevier, vol. 154(1), pages 57-70, April.
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