New formulations and branch-and-cut procedures for the longest induced path problem

Given an undirected graph G=(V,E), the longest induced path problem (LIPP) consists of obtaining a maximum cardinality subset W⊆V such that W induces simple in G. In this paper, we propose two new formulations with exponential number constraints for problem, together effective branch-and-cut procedures its solution. While first formulation (cec) is based on explicitly eliminate cycles, second one (cut) ensures connectivity via cutset constraints. We compare, both theoretically and experimentally, newly proposed approaches state-of-the-art recently literature. More specifically, show polyhedra defined by cut available literature are same. Besides, these stronger theory than cec. also procedure using formulations. Computational experiments cec, although less strong from theoretical point view, best performing approach as it can solve all but 1065 benchmark instances used within given time limit. addition, our outperform when comes to median times optimality. Furthermore, perform extended computational considering more challenging hard-to-solve larger evaluate impacts results offering initial feasible solutions (warm starts)