Abstract
We derive a polynomial time algorithm to compute a stable solution in a mixed matching market from an auction procedure as presented by Eriksson and Karlander [5]. As a special case we derive an \(\mathcal{O}(nm)\) algorithm for bipartite matching that does not seem to have appeared in the literature yet.
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Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice-Hall, Englewood Cliffs (1993)
Demange, G., Gale, D., Sotomayor, M.: Multiitem auctions. Journal of Political Economy 94(4), 863–872 (1986)
Deng, X., Papadimitriou, C.H.: On the complexity of cooparative game solution concepts. Mathematics of Operations Research 19, 257–266 (1994)
Deng, X., Ibaraki, T., Nagamochi, H.: Combinatorial optimization games. In: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, pp. 720–729 (1997)
Eriksson, K., Karlander, J.: Stable matching in a common generalization of the marriage and assignment models. Discrete Mathematics 217(1-3), 135–156 (2000)
Faigle, U., Fekete, S.P., Hochstättler, W., Kern, W.: On the complexity of testing membership in the core of min cost spanning tree games. International Journal of Game Theory 26, 361–366 (1997)
Ford, L.R., Fulkerson, D.R.: A simple algorithm for finding maximal network flows and an application to the hitchcock problem. Canadian Journal of Mathematics 9, 210–218 (1957)
Frank, A.: On Kuhn’s Hungarian method – A tribute from Hungary. Technical report, Egerváry Research Group on Combinatorial Optimization (October 2004)
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)
Galil, Z.: Efficient algorithms for finding maximum matchings in graphs. ACM Computing Surveys 18(1), 23–38 (1986)
Gusfield, D., Irving, R.W.: The stable marriage problem: Structure and algorithms. MIT Press, Cambridge (1989)
Hochstättler, W., Jin, H., Nickel, R.: The hungarian method in a mixed matching market. Technical report, FernUniversität in Hagen, Germany (October 2005)
Knuth, D.E.: Stable marriage and its relation to other combinatorial problems. In: CRM Proceedings and Lecture Notes, vol. 10. American Mathematical Society (1997)
Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Research Logistics Quaterly 2, 83–97 (1955)
Kuhn, H.W.: Variants of the Hungarian method for the assignment problem. Naval Research Logistics Quaterly 3, 253–258 (1956)
Roth, A.E., Sotomayor, M.: Stable outcomes in discrete and continuous models of two-sided matching: A unified treatment. Revista de Econometria, The Brazilian Review of Econometrics 16(2) (November 1996)
Shapley, L.S., Shubik, M.: The assignment game I: The core. International Journal of Game Theory 1, 111–130 (1972)
Sotomayor, M.: Existence of stable outcomes and the lattice property for a unified matching market. Mathematical Social Sciences 39, 119–132 (2000)
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Hochstättler, W., Jin, H., Nickel, R. (2006). Note on an Auction Procedure for a Matching Game in Polynomial Time. In: Cheng, SW., Poon, C.K. (eds) Algorithmic Aspects in Information and Management. AAIM 2006. Lecture Notes in Computer Science, vol 4041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11775096_36
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DOI: https://doi.org/10.1007/11775096_36
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