An Equivalent QUBO Model to the Minimum Multi-Way Cut Problem

Motivated by an application in Computer Vision, we present an efficient QUBO solution for the minimum multi-way cut problem. For an edge-weighted input graph G = (V, E) and a set of terminals T = {t(1), t(2), ... , t(k)} C V we want to find a subset of edges E-c of minimum total cost such that G' = G\ E(c )separates T. QUBO representations are useful for solving problems on an adiabatic quantum computer like those produced by D-Wave Systems. Our reduction from the multi-way cut problem requires only O(k|V|) binary variables/qubits. The main result of this paper is a proof of correctness of this model. Furthermore, our reduction is small enough to be able to empirically test it with an existing D-Wave hybrid quantum-classical solver, which is illustrated at the end of this paper.