Approximation Algorithms for Orienteering and Discounted-Reward TSP

In this paper, we give the rst constant-factor approximationalgorithmfor the rooted Orienteering problem, as well as a new problem that we call the Discounted-Reward TSP, motivated by robot navigation. In both problems, we are given a graph with lengths on edges and prizes (rewards) on nodes, and a start node s. In the Orienteering Problem, the goal is to nd a path that maximizes the reward collected, subject to a hard limit on the total length of the path. In the Discounted-Reward TSP, instead of a length limit we are given a discount factor , and the goal is to maximize total discounted reward collected, where reward for a node reached at time t is discounted by t . This is similar to the objective considered in Markov Decision Processes (MDPs) except we only receive a reward the rst time a node is visited. We also consider tree and multiple-path variants of these problems and provide approximations for those as well. Although the unrooted orienteering problem, where there is no xed...

• Type: Conference
• Year: 2003
• Where: FOCS
• Authors: Avrim Blum, Shuchi Chawla, David R. Karger, Terran Lane, Adam Meyerson, Maria Minkoff
• Keywords: Discounted-Reward TSP, FOCS 2003, Orienteering Problem, Start Node, Theoretical Computer Science