The Maximum Labeled Path Problem

Basile Couëtoux (1) , Elie Nakache (1) , Yann Vaxès (1)

1 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle

In this paper, we study the approximability of the Maximum Labeled Path problem: given a vertex-labeled directed acyclic graph D, find a path in D that collects a maximum number of distinct labels. For any epsilon > 0, we provide a polynomial time approximation algorithm that computes a solution of value at least OPT^{1−epsilon) and a self-reduction showing that any constant ratio approximation algorithm for this problem can be converted into a PTAS. This last result, combined with the APX-hardness of the problem, shows that the problem cannot be approximated within any constant ratio unless P = NP.

Domaines: Algorithme et structure de données [cs.DS]

Basile Couëtoux, Elie Nakache, Yann Vaxès. The Maximum Labeled Path Problem. Algorithmica, 2017, 78 (1), pp.298 - 318. ⟨10.1007/s00453-016-0155-6⟩. ⟨hal-01769613⟩