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On the Hamming distance in combinatorial optimization problems on hypergraph matchings

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Abstract

In this note we consider the properties of the Hamming distance in combinatorial optimization problems on hypergraph matchings, also known as multidimensional assignment problems. It is shown that the Hamming distance between feasible solutions of hypergraph matching problems can be computed as an optimal value of linear assignment problem. For random hypergraph matching problems, an upper bound on the expected Hamming distance to the optimal solution is derived, and an exact expression is obtained in the special case of multidimensional assignment problems with 2 elements in each dimension.

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Authors and Affiliations

  1. AFRL/RWGN-NRC, 101 West Eglin Blvd, Eglin AFB, FL, 32547, USA

    Alla Kammerdiner

  2. Department of Mechanical and Industrial Engineering, University of Iowa, 3131 Seamans Center, Iowa City, IA, 52242, USA

    Pavlo A. Krokhmal

  3. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, 303 Weil Hall, Gainesville, FL, 32611, USA

    Panos M. Pardalos

Authors
  1. Alla Kammerdiner
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  2. Pavlo A. Krokhmal
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  3. Panos M. Pardalos
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Correspondence to Pavlo A. Krokhmal.

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Kammerdiner, A., Krokhmal, P.A. & Pardalos, P.M. On the Hamming distance in combinatorial optimization problems on hypergraph matchings. Optim Lett 4, 609–617 (2010). https://doi.org/10.1007/s11590-010-0187-9

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  • DOI: https://doi.org/10.1007/s11590-010-0187-9

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