On exact solution approaches for the longest induced path problem

Exact and approximate algorithms for the longest induced path problem

“…Let G = (V, E) be an undirected graph defined by its set of n vertices V = {1, • • • , n} and its edge set E ⊆ V × V . For any subset of vertices S ⊆ V , let G[S] = (S, E ) denote the subgraph induced by S in G, where E contains all edges from E that have both of their endpoints in S. The longest induced path problem (LIPP) is defined as that of finding the subset S ⊆ V of largest cardinality such that the resulting induced subgraph, G[S], is a simple path [13].…”

“…In these cases, some subset of vertices cannot transmit a message in a communication network or cannot serve as a transshipment point in a transportation network and, consequently, detours or alternative shortest paths must be used. In other words, the objective of the longest induced path problem is to identify the worst possible case for the shortest distance between any two vertices in the graph, given that these vertices remain connected by some path while the rest of the vertices may fail [13].…”

“…Another interesting interpretation of LIPP appears in social networks with information cascades. Matsypura et al [13] observed that an optimal solution of the longest induced path problem in this context provides the longest possible path of information transmission, where one end vertex of the path corresponds to the seed of the information cascade and the other end vertex is the last to learn this piece of information.…”

“…Although the longest induced path problem belongs to an interesting class of network optimization problems with practical applications in various network contexts, the literature on solution approaches for this problem is rather limited, possibly due to its inherent computational complexity. Matsypura et al [13] were the first to develop exact solution approaches for the longest induced path problem for general graphs, based on integer programming (IP) techniques. They proposed four IP formulations based on three conceptually different interpretations of the problem.…”

“…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.…”