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A MILP model for the connected multidimensional maximum bisection problem

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  • Zoran Lj. Maksimović

    (University of Defence)

Abstract

The Maximum Bisection Problem (MBP) is a well-known combinatorial optimization problem that has been proven to be NP-hard. The maximum bisection of a graph is the partition of its set of vertices into two subsets with an equal number of vertices, where the weight of the edge cut is maximal. This work introduces a connected multidimensional generalization of the Maximum Bisection Problem. In this NP-hard problem, weights on edges are vectors of non-negative numbers, and subgraphs induced by partitions must be connected. A mixed integer linear programming (MILP) formulation is proposed with proof of its correctness. The MILP formulation of the problem has a polynomial number of variables and constraints

Suggested Citation

  • Zoran Lj. Maksimović, 2024. "A MILP model for the connected multidimensional maximum bisection problem," Journal of Combinatorial Optimization, Springer, vol. 48(4), pages 1-17, November.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:4:d:10.1007_s10878-024-01220-z
    DOI: 10.1007/s10878-024-01220-z
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    References listed on IDEAS

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    1. Raidl, Günther R., 2015. "Decomposition based hybrid metaheuristics," European Journal of Operational Research, Elsevier, vol. 244(1), pages 66-76.
    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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