The Maximum Labeled Path Problem
Résumé
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.
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