Algorithms for the On-Line Quota Traveling Salesman Problem

Giorgio Ausiello (1) , Marc Demange (2) , L. Laura (1) , Vangelis Th. Paschos (3)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 ESSEC Business School
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the travelling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performance in the usual framework of the competitive analysis. In particular we present a 2-competitive algorithm that matches the lower bound for general metric spaces. In the case of the half-line metric space, we show that it is helpful not to move at full speed, and this approach is also used to derive the best on-line polynomial time algorithm known so far for the more general On-Line TSP problem (in the homing version).

Domaines: Complexité [cs.CC]; Mathématique discrète [cs.DM]

Giorgio Ausiello, Marc Demange, L. Laura, Vangelis Th. Paschos. Algorithms for the On-Line Quota Traveling Salesman Problem. 2004. ⟨hal-00004070⟩