Approximation of the Constrained Path Covering Problem

Laurent Alfandari (1, 2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 ESSEC Business School

We study a generic covering problem frequently met in transportation planning. The problem is to cover a set of tasks by constrained paths, representing routings of commodities, so that the total cost of selected paths is minimal. In this paper, paths are constrained to have limited weight and limited number of tasks. We show that the generic problem is NP-hard and that a greedy heuristic using dynamic programming at each step achieves an approximation ratio of ln(d), where d is the maximum number of tasks of a path.

Mots clés: transportation planning; constrained path; set covering; dynamic programming; approximation

Domaines: Recherche opérationnelle [math.OC]

Laurent Alfandari. Approximation of the Constrained Path Covering Problem. 2007. ⟨hal-00174878⟩