
CMUCS03121
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS03121
Approximation Algorithms for Orienteering
and DiscountedReward TSP
Avrim Blum, Shuchi Chawla, David R. Karger*,
Terran Lane**, Adam Meyerson, Maria Minkoff*
March 2003
CMUCS03121.ps
CMUCS03121.pdf
Keywords: Approximation algorithms, traveling salesman problem,
prize collecting TSP, orienteering, robot navigation, Markov Decision
Processes
In this paper, we give the first constantfactor approximation
algorithm for the rooted Orienteering problem, as well as a new
problem that we call the DiscountedReward 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 find a path that maximizes the
reward collected, subject to a hard limit on the total length of the
path. In the DiscountedReward TSP, instead of a length limit we are
given a discount factor &gamma, and the goal is to maximize total
discounted reward collected, where reward for a node reached at time
t is discounted by &gamma^{t}. This is similar to the objective
considered in Markov Decision Processes (MDPs) except we only receive
reward the first time a node is visited. We also consider several
treevariants on these problems and provide approximations for those
as well. Although the unrooted orienteering problem, where there is
no fixed start node s, has been known to be approximable using
algorithms for related problems such as kTSP (in which the amount
of reward to be collected is fixed and the total length is
approximately minimized), ours is the first to approximate the rooted
question, solving a wellknown open problem.
14 pages
*MIT Laboratory for Computer Science, Massachusetts Institute of Technology
**Department of Computer Science, University of New Mexico.
