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Algorithmica

, Volume 78, Issue 1, pp 298–318 | Cite as

The Maximum Labeled Path Problem

  • Basile Couëtoux
  • Elie Nakache
  • Yann VaxèsEmail author
Article

Abstract

In this paper, we study the approximability of the Maximum Labeled Path problem: given a vertex-labeled directed acyclic graph D, find a path in D that collects a maximum number of distinct labels. For any \(\epsilon >0\), we provide a polynomial time approximation algorithm that computes a solution of value at least \(OPT^{1-\epsilon }\) and a self-reduction showing that any constant ratio approximation algorithm for this problem can be converted into a PTAS. This last result, combined with the APX-hardness of the problem, shows that the problem cannot be approximated within any constant ratio unless \(P=NP\).

Keywords

Graph algorithm Approximation algorithm Hardness of approximation Labels 

Notes

Acknowledgments

We are grateful to Jérôme Monnot for suggesting the use of a self-reduction to prove the hardness result of Sect. 3.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.CNRS, LIF UMR 7279Aix-Marseille UniversitéMarseilleFrance

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