Abstract

We study a variety of geometric network optimization problems on a set of points, in which we are given a resource bound, B, on the total length of the network, and our objective is to maximize the number of points visited (or the total "value" of points visited). In particular, we resolve the well-publicized open problem on the approximability of the rooted "orienteering problem" for the case in which the sites are given as points in the plane and the network required is a cycle. We obtain a 2-approximation for this problem. We also obtain approximation algorithms for variants of this problem in which the network required is a tree (3-approximation) or a path (2-approximation). No prior approximation bounds were known for any of these problems. We also obtain improved approximation algorithms for geometric instances of the unrooted orienteering problem, where we obtain a 2-approximation for both the cycle and tree versions of the problem on points in the plane, as well as a ...

Citations