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A rearrangement of adjacency matrix based approach for solving the crossing minimization problem

Author

Listed:
  • Neng Fan

    (University of Florida)

  • Panos M. Pardalos

    (University of Florida)

Abstract

In this paper, we first present a binary linear programming formulation for the crossing minimization problem (CMP) in bipartite graphs. Then we use the models of a modified minimum cost flow problem (MMCF) and a travelling salesman problem (TSP) to approximatively solve the CMP by rearranging the adjacency matrix of the bipartite graph. Our approaches are useful for problems defined on dense bipartite graphs. In addition, we compute the exact crossing numbers for some general dense graphs.

Suggested Citation

  • Neng Fan & Panos M. Pardalos, 2011. "A rearrangement of adjacency matrix based approach for solving the crossing minimization problem," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 747-762, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9326-6
    DOI: 10.1007/s10878-010-9326-6
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    References listed on IDEAS

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    1. Christoph Buchheim & Angelika Wiegele & Lanbo Zheng, 2010. "Exact Algorithms for the Quadratic Linear Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 168-177, February.
    2. Valls, Vicente & Marti, Rafael & Lino, Pilar, 1996. "A branch and bound algorithm for minimizing the number of crossing arcs in bipartite graphs," European Journal of Operational Research, Elsevier, vol. 90(2), pages 303-319, April.
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    Cited by:

    1. Palubeckis, Gintaras & Tomkevičius, Arūnas & Ostreika, Armantas, 2019. "Hybridizing simulated annealing with variable neighborhood search for bipartite graph crossing minimization," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 84-101.

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