The Maximum Labeled Path Problem

  • Basile CouëtouxEmail author
  • Elie Nakache
  • Yann Vaxès
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)


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. Our main results are a \(\sqrt{OPT}\)-approximation algorithm for this problem 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 a constant ratio unless \(P=NP\).


Approximation Algorithm Polynomial Time Network Design Problem Label Function Maximal Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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 International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Aix-Marseille Université, CNRS, LIF UMR 7279MarseilleFrance

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