A MILP model for the connected multidimensional maximum bisection problem

Zoran Lj. Maksimović ()
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Zoran Lj. Maksimović: University of Defence

Journal of Combinatorial Optimization, 2024, vol. 48, issue 4, No 6, 17 pages

Abstract: 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

Keywords: Graph bisection; Mixed integer linear programming; Combinatorial optimization; Multidimensional weight of edge; Connected graphs; 90C27; 05C40 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01220-z

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