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 APX-hardness of the problem, shows that the problem cannot be approximated within a constant ratio unless \(P=NP\).
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Batten, L.M.: Combinatorics of Finite Geometries. Cambridge University Press, New York (1997)
Broersma, H., Li, X.: Spanning trees with many or few colors in edge-colored graphs. Discuss. Math. Graph Theory 17, 259–269 (1997)
Broersma, H., Li, X., Woeginger, G.J., Zhang, S.: Paths and cycles in colored graphs. Aust. J. Comb. 31, 299–311 (2005)
Brüggemann, T., Monnot, J., Woeginger, G.J.: Local search for the minimum label spanning tree problem with bounded color classes. Oper. Res. Lett. 31, 195–201 (2003)
Chang, R.-S., Leu, S.-J.: The minimum labeling spanning trees. IPL 31, 195–201 (2003)
Couëtoux, B., Gourvès, L., Monnot, J., Telelis, O.: Labeled traveling salesman problems: complexity and approximation. Discrete Optim. 7, 74–85 (2010)
Hassin, R., Monnot, J., Segev, D.: Approximation algorithms and hardness results for labeled connectivity problems. J. Comb. Optim. 14, 437–453 (2007)
Hassin, R., Monnot, J., Segev, D.: The complexity of bottleneck labeled graph problems. In: Brandstädt, A., Kratsch, D., Müller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 328–340. Springer, Heidelberg (2007)
Håstad, J.: Some optimal inapproximability results. J. ACM 48, 798–859 (2001)
Krumke, S.O., Wirth, H.-C.: Approximation algorithms and hardness results for labeled connectivity problems. IPL 66, 81–85 (1998)
Monnot, J.: The labeled perfect matching in bipartite graphs. IPL 96, 81–88 (2005)
Acknowledgment
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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Couëtoux, B., Nakache, E., Vaxès, Y. (2014). The Maximum Labeled Path Problem. In: Kratsch, D., Todinca, I. (eds) Graph-Theoretic Concepts in Computer Science. WG 2014. Lecture Notes in Computer Science, vol 8747. Springer, Cham. https://doi.org/10.1007/978-3-319-12340-0_13
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DOI: https://doi.org/10.1007/978-3-319-12340-0_13
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