Approximation algorithms for deadline-TSP and vehicle routing with time-windows

Abstract

Given a metric space G on n nodes, with a start node r and deadlines D(v) for each vertex v, we consider the Deadline-TSP problem of finding a path starting at r that visits as many nodes as possible by their deadlines. We also consider the more general Vehicle Routing with TimeWindows problem, in which each node v also has a releasetime R(v) and the goal is to visit as many nodes as possible within their "time-windows" [R(v), D(v)]. No good approximations were known previously for these problems on general metric spaces. We give an O(log n) approximation algorithm for Deadline-TSP, and extend this algorithm to an O(log 2 n) approximation for the Time-Window problem. We also give a bicriteria approximation algorithm for both problems: Given an > 0, our algorithm produces a log(1/ ) approximation, while exceeding the deadlines by a factor of 1 + . We use as a subroutine for these results a constantfactor approximation that we develop for a generalization of the orienteering problem in which both the start and the end nodes of the path are fixed. In the process, we give a 3-approximation to the orienteering problem, improving on the previously best known 4-approximation of [6].

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