A connected multidimensional maximum bisection problem

TL;DR

This paper introduces a new connected multidimensional version of the maximum graph bisection problem, where edge weights are vectors and partitions must be connected, along with a polynomial-sized MILP formulation.

Contribution

It extends the classic maximum bisection problem to a multidimensional, connected variant and provides a correct, polynomial-sized mixed integer linear programming formulation.

Findings

MILP formulation is correct and polynomial in size

The problem generalizes maximum bisection to multidimensional edge weights

Connectedness constraint is incorporated into the formulation

Abstract

The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal number of vertices, and the weight of the edge cut is maximal. This work introduces a connected multidimensional generalization of the maximum bisection problem. In this problem the weights on edges are vectors of positive numbers rather than numbers and partitions should be connected. A mixed integer linear programming formulation is proposed with the proof of its correctness. The MILP formulation of the problem has polynomial number of variables and constraints.