The orienteering problem in the plane revisited

Abstract

We consider the orienteering problem: Given a set P of n points in the plane, a starting point r ∈ P, and a length constraint B, one needs to find a tour starting at r that visits as many points of P as possible and of length not exceeding B. We present a (1−ε)-approximation algorithm for this problem that runs in nO(1/ε) time, and visits at least (1−ε)kopt points of P, where kopt is the number of points visited by the optimal solution. This is the first polynomial time approximation scheme (PTAS) for this problem. The algorithm also works in higher dimensions.