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Improved algorithms for orienteering and related problems

Authors:

Chandra Chekuri,

Martin PálAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 8, Issue 3

Article No.: 23, Pages 1 - 27

https://doi.org/10.1145/2229163.2229167

Published: 24 July 2012 Publication History

Abstract

In this article, 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 time limit 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. Orienteering with time-windows is the more general problem in which each node v has a specified time-window [R(v), D(v)] and a node v is counted as visited by the walk only if v is visited during its time-window. We design new and improved algorithms for the orienteering problem and orienteering with time-windows. Our main results are the following:

— A (2+ϵ) approximation for orienteering in undirected graphs, improving upon the 3-approximation of Bansal et al. [2004].

— An O(log² OPT) approximation for orienteering in directed graphs, where OPT ≤ n is the number of vertices visited by an optimal solution. Previously, only a quasipolynomial-time algorithm due to Chekuri and Pál [2005] achieved a polylogarithmic approximation (a ratio of O(log OPT)).

— Given an α approximation for orienteering, we show an O(α ċ max{log OPT, log l_max/l_min}) approximation for orienteering with time-windows, where l_max and l_min are the lengths of the longest and shortest time-windows respectively.

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Index Terms

Improved algorithms for orienteering and related problems
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
      1. Network flows
  2. Randomness, geometry and discrete structures

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 8, Issue 3

July 2012

257 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2229163

Issue’s Table of Contents

Copyright © 2012 ACM.

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Association for Computing Machinery

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Publication History

Published: 24 July 2012

Accepted: 01 February 2010

Revised: 01 December 2009

Received: 01 May 2009

Published in TALG Volume 8, Issue 3

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