Improved algorithms for orienteering and related problems

Chandra Chekuri, Nitish Korula, Martin Pál

Abstract: In this paper we consider the orienteering problem in undirected and directed graphs and obtain improved approximation algorithms. The point to point-orienteering-problem is the following: Given an edge-weighted graph G = (V, E) (directed or undirected), two nodes s, t ∈ V and a budget B, find an s-t walk in G of total length at most B that maximizes the number of distinct nodes visited by the walk. This problem is closely related to tour problems such as TSP as well as network design problems such as k-MST. Our main results are the following.• A 2 + ε approximation in undirected graphs, improving upon the 3-approximation from [6].• An O(log2 OPT) approximation in directed graphs. Previously, only a quasi-polynomial time algorithm achieved a poly-logarithmic approximation [14] (a ratio of O (log OPT)).The above results are based on, or lead to, improved algorithms for several other related problems.