Algorithms for the on-line quota traveling salesman problem

The Quota Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of 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 competitive analysis. In particular we present a 2-competitive algorithm that matches the lower bound for general metric spaces. In the case of the halfline 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 On-Line TSP (in the homing version).