Abstract
In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V,E) with n vertices with a color (or label) function L : E→ {c 1,...,c q }, the labeled maximum matching problem consists in finding a maximum matching on G that uses a minimum or a maximum number of colors.
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References
Albert, M., Frieze, A., Reed, B.: Multicoloured Hamilton cycles. Electron. J. Combin. 2 (1995) (Research Paper 10)
Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoretical Computer Science 237, 123–134 (2000)
Williamson, D.P.: Improved Approximation Algorithms for MAX SAT. Journal of Algorithms 42(1), 173–202 (2002)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation (Combinatorial Optimization Problems and Their Approximability Properties). Springer, Berlin (1999)
Berman, P., Karpinski, M., Scott, A.D.: Approximation Hardness of Short Symmetric Instances of MAX-3SAT. ECCC TR-03-049 (2003)
Berman, P., Karpinski, M.: On Some Tighter Inapproximability Results. ECCC TR-05-029 (1998)
Broersma, H., Li, X.: Spanning trees with many or few colors in edgecolored graphs. Discussiones Mathematicae Graph Theory 17(2), 259–269 (1997)
Broersma, H., Li, X., Woeginger, G.J., Zhang, S.: Paths and cycles in colored graphs. Australasian J. Combin. 31 (2005)
Brüggemann, T., Monnot, J., Woeginger, G.J.: Local search for the minimum label spanning tree problem with bounded color classes. Operations Research Letters 31(3), 195–201 (2003)
Cameron, K.: Coloured matchings in bipartite graphs. Discrete Mathematics 169, 205–209 (1997)
Carr, R.D., Doddi, S., Konjevod, G., Marathe, M.V.: On the red-blue set cover problem. In: SODA, pp. 345–353 (2000)
Chang, R.-S., Leu, S.-J.: The minimum labeling spanning trees. Information Processing Letters 63, 277–282 (1997)
Costa, M.C., de Werra, D., Picouleau, C., Ries, B.: Bicolored matchings in some classes of graphs. Technical report (2004)
Erdös, P., Nešetřil, J., Rödl, V.: On some problems related to partitions of edges of a graph. In: Graphs and other combinatorial topics, Teubner, Leipzig, pp. 54–63 (1983)
Feige, U.: A threshold of for approximating set cover. J. ACM 45, 634–652 (1998)
Frieze, A., Reed, B.: Polychromatic Hamilton cycles. Discrete Math. 118, 69–74 (1993)
Itai, A., Rodeh, M., Tanimoto, S.: Some matching problems in bipartite graphs. J. ACM 25(4), 517–525 (1978)
Karpinski, M.: Personnal communication (2005)
Krumke, S.O., Wirth, H.-C.: On the minimum label spanning tree problem. Information Processing Letters 66, 81–85 (1998)
Marathe, M.V., Ravi, S.S.: On Approximation Algorithms for the Minimum Satisfiability Problem. Information Processing Letters 58(1), 23–29 (1996)
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. of Comp. and Sys. Sci. 43, 425–440 (1991)
Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and sub-constant error-probability PCP characterization of NP. In: Proc. 29th Ann. ACM Symp. on Theory of Comp., pp. 475–484. ACM, New York (1997)
Wan, Y., Chen, G., Xu, Y.: A note on the minimum label spanning tree. Information Processing Letters 84, 99–101 (2002)
Xiong, Y., Golden, B., Wasil, E.: Worst-case behavior of the MVCA heuristic for the minimum labeling spanning tree problem. Operations Research Letters 33(1), 77–80 (2005)
Yi, T., Murty, K.G., Spera, C.: Matchings in colored bipartite networks. Discrete Applied Mathematics 121(1-3), 261–277 (2002)
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Monnot, J. (2005). On Complexity and Approximability of the Labeled Maximum/Perfect Matching Problems. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_93
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DOI: https://doi.org/10.1007/11602613_93
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30935-2
Online ISBN: 978-3-540-32426-3
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