The Maximum Labeled Path Problem

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 > 0, we provide a polynomial time approximation algorithm that computes a solution of value at least OP T 1− 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 = N P .
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Submitted on : Wednesday, April 18, 2018 - 11:34:50 AM
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Basile Couëtoux, Elie Nakache, Yann Vaxès. The Maximum Labeled Path Problem. Algorithmica, Springer Verlag, 2017, 78 (1), pp.298 - 318. ⟨10.1007/s00453-016-0155-6⟩. ⟨hal-01769613⟩

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