Riassunto
Il matching pesato su grafi non bipartiti è uno dei i problemi più “difficili” di ottimizzazione combinatoria che può essere risolto in tempo polinomiale. Estenderemo l’Algoritmo del Matching di Edmonds al caso pesato ottenendo ancora un’implementazione di complessità O(n 3). Questo algoritmo ha molte applicazioni, alcune delle quali sono citate negli esercizi e nella Sezione 12.2. Esistono due formulazioni del problema del matching pesato:
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Riferimenti bibliografici
Letteratura generale
Gerards, A.M.H. [1995]: Matching. In: Handbooks in Operations Research and Management Science; Volume 7: Network Models (M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser, eds.), Elsevier, Amsterdam, pp. 135–224
Lawler, E.L. [1976]: Combinatorial Optimization; Networks and Matroids. Holt, Rinehart and Winston, New York, Chapters 5 and 6
Papadimitriou, C.H., Steiglitz, K. [1982]: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, Chapter 11
Pulleyblank, W.R. [1995]: Matchings and extensions. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam
Riferimenti citati
Balinski, M.L. [1972]: Establishing the matching polytope. Journal of Combinatorial Theory 13, 1–13
Ball, M.O., Derigs, U. [1983]: An analysis of alternative strategies for implementing matching algorithms. Networks 13, 517–549
Birkhoff, G. [1946]: Tres observaciones sobre el algebra lineal. Revista Universidad Nacional de Tucumán, Series A 5, 147–151
Burkard, R., Dell’Amico, M., Martello, S. [2009]: Assignment Problems. SIAM, Philadelphia
Cook, W., Rohe, A. [1999]: Computing minimum-weight perfect matchings. INFORMS Journal of Computing 11, 138–148
Cunningham, W.H., Marsh, A.B. [1978]: A primal algorithm for optimum matching. Mathematical Programming Study 8, 50–72
Edmonds, J. [1965]: Maximum matching and a polyhedron with (0,1) vertices. Journal of Research of the National Bureau of Standards B 69, 125–130
Egerváry, E. [1931]: Matrixok kombinatorikus tulajdonságairol. Matematikai és Fizikai Lapok 38, 16–28 [in Hungarian]
Gabow, H.N. [1973]: Implementation of algorithms for maximum matching on non-bipartite graphs. Ph.D. Thesis, Stanford University, Dept. of Computer Science
Gabow, H.N. [1976]: An efficient implementation of Edmonds’ algorithm for maximum matching on graphs. Journal of the ACM 23, 221–234
Gabow, H.N. [1990]: Data structures for weighted matching and nearest common ancestors with linking. Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, 434–443
Grötschel, M., Pulleyblank, W.R. [1981]: Weakly bipartite graphs and the max-cut problem. Operations Research Letters 1, 23–27
Kuhn, H.W. [1955]: The Hungarian method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97
Lipton, R.J., Tarjan, R.E. [1979]: A separator theorem for planar graphs. SIAM Journal on Applied Mathematics 36, 177–189
Lipton, R.J., Tarjan, R.E. [1980]: Applications of a planar separator theorem. SIAM Journal on Computing 9, 615–627
Lovász, L. [1979]: Graph theory and integer programming. In: Discrete Optimization I; Annals of Discrete Mathematics 4 (P.L. Hammer, E.L. Johnson, B.H. Korte, eds.), North-Holland, Amsterdam, pp. 141–158
Mehlhorn, K., Schäfer, G. [2000]: Implementation of O(nm log n) weighted matchings in general graphs: the power of data structures. In: Algorithm Engineering; WAE-2000; LNCS 1982 (S. Näher, D. Wagner, eds.), pp. 23–38; also electronically in The ACM Journal of Experimental Algorithmics 7
Monge, G. [1784]: Mémoire su r la théorie des déblais et des remblais. Histoire de l’AcadémieRoyale des Sciences 2, 666–704
Munkres, J. [1957]: Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics 5, 32–38
von Neumann, J. [1953]: A certain zero-sum two-person game equivalent to the optimal assignment problem. In: Contributions to the Theory of Games II; Ann. of Math. Stud. 28 (H.W. Kuhn, ed.), Princeton University Press, Princeton, pp. 5–12
Schrijver, A. [1983a]: Short proofs on the matching polyhedron. Journal of Combinatorial Theory B 34, 104–108
Schrijver, A. [1983b]: Min-max results in combinatorial optimization. In: Mathematical Programming; The State of the Art — Bonn 1982 (A. Bachem, M. Grötschel, B. Korte, eds.), Springer, Berlin, pp. 439–500
Varadarajan, K.R. [1998]: A divide-and-conquer algorithm for min-cost perfect matching in the plane. Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, 320–329
Weber, G.M. [1981]: Sensitivity analysis of optimal matchings. Networks 11, 41–56
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Korte, B., Vygen, J. (2011). Matching Pesato. In: Ottimizzazione Combinatoria. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-1523-4_11
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