Improved algorithms for orienteering and related problems

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 <i>G</i> = (<i>V, E</i>) (directed or undirected), two nodes <i>s, t</i> ∈ <i>V</i> and a budget <i>B</i>, find an <i>s-t walk</i> in <i>G</i> of total length at most <i>B</i> 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 <i>k</i>-MST. Our main results are the following. • A 2 + ε approximation in undirected graphs, improving upon the 3-approximation from [6]. • An <i>O</i>(log<sup>2</sup> OPT) approximation in directed graphs. Previously, only a quasi-polynomial time algorithm achieved a poly-logarithmic approximation [14] (a ratio of <i>O</i> (log OPT)). The above results are based on, or lead to, improved algorithms for several other related problems.

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