An Experimental Study of ILP Formulations for the Longest Induced Path Problem

Exact and approximate algorithms for the longest induced path problem

“…Bökler et al [5] proposed new integer linear programming formulations for the longest induced path problem, based on cut or subtour elimination constraints, exact separation routines, relaxation of variables and clique constraints. They obtain strictly stronger relaxations than those proposed in [13].…”

“…However, this formulation is not enough, because it still allows solutions formed by multiple disjoint cycles, only one of them containing vertex s. In order to obtain a longest single cycle through s yielding the longest induced path, one has to enforce that the graph induced by the optimal y-variables be connected. Bökler et al [5] explored two strategies to achieve connectivity, by augmenting ILP Base with cut or (generalized) subtour elimination constraints. Let δ * (W ) = {(w,w) ∈ E * : w ∈ W,w ∈ V * \ W } be the set of edges in the cut induced by W ⊆ V * .…”

“…In this section, we present computational experiments with the exact algorithm and the new heuristic proposed in Section 3 and the algorithms of Matsypura et al [13] and Bökler et al [5].…”

“…In addition, they provided an exact iterative algorithm that solves a sequence of smaller MIPs and developed a randomized heuristic to find induced paths in large networks. Bökler et al [5] proposed stronger integer linear programming formulations using cut (or generalized subtour elimination) constraints and clique inequalities.…”

“…We propose an exact enumerative algorithm and a heuristic for the problem. We review in Section 2 the existing solutions approaches proposed by Matsypura et al [13] and Bökler et al [5], from where we take the same test instances that will be used in our computational experiments. Section 3 describes the proposed exact enumerative algorithm and a new heuristic.…”