# The Maximum Labeled Path Problem

1 ACRO - Algorithmique, Combinatoire et Recherche Opérationnelle
LIS - Laboratoire d'Informatique et Systèmes
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. 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 {\sc APX}-hardness of the problem, shows that the problem cannot be approximated within a constant ratio unless $P=NP$.
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-01195672
Contributor : Yann Vaxès <>
Submitted on : Tuesday, September 8, 2015 - 11:55:29 AM
Last modification on : Thursday, December 19, 2019 - 2:11:06 AM

### Citation

Basile Couëtoux, Elie Nakache, Yann Vaxès. The Maximum Labeled Path Problem. 40th International Workshop, WG 2014, Jun 2014, Nouan-le-Fuzelier, France. pp.152-163, ⟨10.1007/978-3-319-12340-0_13⟩. ⟨hal-01195672⟩

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