Abstract
Consider a bipartite graph with a set of left-vertices and a set of right-vertices. All the edges adjacent to the same left-vertex have the same weight. We present an algorithm that, given the set of right-vertices and the number of left-vertices, processes a uniformly random permutation of the left-vertices, one left-vertex at a time. In processing a particular left-vertex, the algorithm either permanently matches the left-vertex to a thus-far unmatched right-vertex, or decides never to match the left-vertex. The weight of the matching returned by our algorithm is within a constant factor of that of a maximum weight matching.
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References
Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete algorithms, pp. 434–443 (January 2007)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Dimitrov, N.B., Plaxton, C.G.: Competitive weighted matching in transversal matroids. Technical Report TR–08–04, Department of Computer Science, University of Texas at Austin (January 2008)
Ferguson, T.: Who solved the secretary problem? Statistical Science 4, 282–289 (1989)
Freeman, P.R.: The secretary problem and its extensions: A review. International Statistical Review 51, 189–206 (1983)
Karger, D.: Random sampling and greedy sparsification for matroid optimizaiton problems. Mathematical Programming 82, 41–81 (1998)
Kleinberg, R.: A multiple-choice secretary algorithm with applications to online auctions. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete algorithms, pp. 630–631 (January 2005)
Lawler, E.: Combinatorial Optimization: Networks and Matroids. Dover Publications, Mineola (2001)
Lindley, D.V.: Dynamic programming and decision theory. Applied Statistics 10, 39–51 (1961)
Oxley, J.: What is a matroid? Cubo. 5, 179–218 (2003)
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Dimitrov, N.B., Plaxton, C.G. (2008). Competitive Weighted Matching in Transversal Matroids. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_33
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DOI: https://doi.org/10.1007/978-3-540-70575-8_33
Publisher Name: Springer, Berlin, Heidelberg
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