Skip to main content

Part of the book series: UNITEXT ((UNITEXTMAT))

  • 523 Accesses

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:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

    Google Scholar 

  • Lawler, E.L. [1976]: Combinatorial Optimization; Networks and Matroids. Holt, Rinehart and Winston, New York, Chapters 5 and 6

    MATH  Google Scholar 

  • Papadimitriou, C.H., Steiglitz, K. [1982]: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, Chapter 11

    MATH  Google Scholar 

  • Pulleyblank, W.R. [1995]: Matchings and extensions. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam

    Google Scholar 

Riferimenti citati

  • Balinski, M.L. [1972]: Establishing the matching polytope. Journal of Combinatorial Theory 13, 1–13

    Article  MathSciNet  MATH  Google Scholar 

  • Ball, M.O., Derigs, U. [1983]: An analysis of alternative strategies for implementing matching algorithms. Networks 13, 517–549

    Article  MathSciNet  MATH  Google Scholar 

  • Birkhoff, G. [1946]: Tres observaciones sobre el algebra lineal. Revista Universidad Nacional de Tucumán, Series A 5, 147–151

    MathSciNet  MATH  Google Scholar 

  • Burkard, R., Dell’Amico, M., Martello, S. [2009]: Assignment Problems. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  • Cook, W., Rohe, A. [1999]: Computing minimum-weight perfect matchings. INFORMS Journal of Computing 11, 138–148

    Article  MathSciNet  MATH  Google Scholar 

  • Cunningham, W.H., Marsh, A.B. [1978]: A primal algorithm for optimum matching. Mathematical Programming Study 8, 50–72

    Article  MathSciNet  Google Scholar 

  • 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

    MathSciNet  MATH  Google Scholar 

  • Egerváry, E. [1931]: Matrixok kombinatorikus tulajdonságairol. Matematikai és Fizikai Lapok 38, 16–28 [in Hungarian]

    MATH  Google Scholar 

  • Gabow, H.N. [1973]: Implementation of algorithms for maximum matching on non-bipartite graphs. Ph.D. Thesis, Stanford University, Dept. of Computer Science

    Google Scholar 

  • Gabow, H.N. [1976]: An efficient implementation of Edmonds’ algorithm for maximum matching on graphs. Journal of the ACM 23, 221–234

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Grötschel, M., Pulleyblank, W.R. [1981]: Weakly bipartite graphs and the max-cut problem. Operations Research Letters 1, 23–27

    Article  MathSciNet  MATH  Google Scholar 

  • Kuhn, H.W. [1955]: The Hungarian method for the assignment problem. Naval Research Logistics Quarterly 2, 83–97

    Article  MathSciNet  Google Scholar 

  • Lipton, R.J., Tarjan, R.E. [1979]: A separator theorem for planar graphs. SIAM Journal on Applied Mathematics 36, 177–189

    Article  MathSciNet  MATH  Google Scholar 

  • Lipton, R.J., Tarjan, R.E. [1980]: Applications of a planar separator theorem. SIAM Journal on Computing 9, 615–627

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Monge, G. [1784]: Mémoire su r la théorie des déblais et des remblais. Histoire de l’AcadémieRoyale des Sciences 2, 666–704

    Google Scholar 

  • Munkres, J. [1957]: Algorithms for the assignment and transportation problems. Journal of the Society for Industrial and Applied Mathematics 5, 32–38

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • Schrijver, A. [1983a]: Short proofs on the matching polyhedron. Journal of Combinatorial Theory B 34, 104–108

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • 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

    Google Scholar 

  • Weber, G.M. [1981]: Sensitivity analysis of optimal matchings. Networks 11, 41–56

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Italia

About this chapter

Cite this chapter

Korte, B., Vygen, J. (2011). Matching Pesato. In: Ottimizzazione Combinatoria. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-1523-4_11

Download citation

Publish with us

Policies and ethics