On Minimal Tree-Inducing Cycle-Cutsets and Their Use in a Cutset-Driven Local Search

We prove that in grids of any size there exists a minimal cycle-cutset that its complement induces a single connected tree. More generally, any cycle-cutset in a grid can be transformed to a tree-inducing cycle-cutset, no bigger than the original one. We use this result to improve the known lower bounds on the size of a minimal cycle-cutset in some cases of grids, thus equating the lower bound to the known upper bound. In addition, we present a cyclecutset driven stochastic local search algorithm in order to approximate the minimal energy of a sum of unary and binary potentials. We show that this method is on-par and even surpasses the state-of-the-art on some grid problems, when both are initialized by elementary means.