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A branch-and-bound algorithm for the minimum cut linear arrangement problem

Author

Listed:
  • Gintaras Palubeckis

    (Kaunas University of Technology)

  • Dalius Rubliauskas

    (Kaunas University of Technology)

Abstract

Given an edge-weighted graph G of order n, the minimum cut linear arrangement problem (MCLAP) asks to find a one-to-one map from the vertices of G to integers from 1 to n such that the largest of the cut values c 1,…,c n−1 is minimized, where c i , i∈{1,…,n−1}, is the total weight of the edges connecting vertices mapped to integers 1 through i with vertices mapped to integers i+1 through n. In this paper, we present a branch-and-bound algorithm for solving this problem. A salient feature of the algorithm is that it employs a dominance test which allows reducing the redundancy in the enumeration process drastically. The test is based on the use of a tabu search procedure developed to solve the MCLAP. We report computational results for both the unweighted and weighted graphs. In particular, we focus on calculating the cutwidth of some well-known graphs from the literature.

Suggested Citation

  • Gintaras Palubeckis & Dalius Rubliauskas, 2012. "A branch-and-bound algorithm for the minimum cut linear arrangement problem," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 540-563, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9406-2
    DOI: 10.1007/s10878-011-9406-2
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    References listed on IDEAS

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    1. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    2. Stefan E. Karisch & Franz Rendl & Jens Clausen, 2000. "Solving Graph Bisection Problems with Semidefinite Programming," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 177-191, August.
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    Cited by:

    1. Santos, Vinícius Gandra Martins & Carvalho, Marco Antonio Moreira de, 2021. "Tailored heuristics in adaptive large neighborhood search applied to the cutwidth minimization problem," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1056-1066.

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