Skip to main content
SpringerLink
Log in

Matroidi

  • Chapter
Ottimizzazione Combinatoria

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

  • 528 Accesses

Riassunto

Molti problemi di ottimizzazione combinatoria possono essere formulati come segue. Data una famiglia di insiemi (E, \( \mathcal{F} \) ), ovvero un insieme finito E e dei sottoinsiemi \( \mathcal{F} \subseteq 2^E \) , e una funzione di costo c: \( \mathcal{F} \to \mathbb{R} \) , trovare un elemento di \( \mathcal{F} \) il cui costo sia minimo o massimo. Nel seguito assumiamo che c sia una funzione modulare, ossia che c(X) = c(∅) + ∑x∈ X (c({x}) − c(∅)) per ogni X ⊆ E; in modo analogo ci è data una funzione c: E → ℝ e scriviamo c(X) = ∑ e ∈ X c(e).

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

Access this chapter

Log in via an institution
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

  • Bixby, R.E., e Cunningham, W.H. [1995]: Matroid optimization and algorithms. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam

    Google Scholar 

  • Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A. [1998]: Combinatorial Optimization. Wiley, New York, Chapter 8

    MATH  Google Scholar 

  • Faigle, U. [1987]: Matroids in combinatorial optimization. In: Combinatorial Geometries (N. White, ed.), Cambridge University Press

    Google Scholar 

  • Gondran, M., Minoux, M. [1984]: Graphs and Algorithms. Wiley, Chichester, Chapter 9

    MATH  Google Scholar 

  • Lawler, E.L. [1976]: Combinatorial Optimization; Networks and Matroids. Holt, Rinehart and Winston, New York, Chapters 7 and 8

    MATH  Google Scholar 

  • Oxley, J.G. [1992]: Matroid Theory. Oxford University Press, Oxford

    MATH  Google Scholar 

  • von Randow, R. [1975]: Introduction to the Theory of Matroids. Springer, Berlin

    Book  MATH  Google Scholar 

  • Recski, A. [1989]: Matroid Theory and its Applications. Springer, Berlin

    Google Scholar 

  • Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin, Chapters 39–42

    MATH  Google Scholar 

  • Welsh, D.J.A. [1976]: Matroid Theory. Academic Press, London

    MATH  Google Scholar 

Riferimenti citati

  • Cunningham, W.H. [1986]: Improved bounds for matroid partition and intersectionx algorithms. SIAM Journal on Computing 15, 948–957

    Article  MathSciNet  MATH  Google Scholar 

  • Edmonds, J. [1970]: Submodular functions, matroids and certain polyhedra. In: Combinatorial Structures and Their Applications; Proceedings of the Calgary International Conference on Combinatorial Structures and Their Applications 1969 (R. Guy, H. Hanani, N. Sauer, J. Schönheim, eds.), Gordon and Breach, New York, pp. 69–87

    Google Scholar 

  • Edmonds, J. [1971]: Matroids and the greedy algorithm. Mathematical Programming 1, 127–136

    Article  MathSciNet  MATH  Google Scholar 

  • Edmonds, J. [1979]: Matroid intersection. In: Discrete Optimization I; Annals of Discrete Mathematics 4 (P.L. Hammer, E.L. Johnson, B.H. Korte, eds.), North-Holland, Amsterdam, pp. 39–49

    Google Scholar 

  • Edmonds, J., Fulkerson, D.R. [1965]: Transversals and matroid partition. Journal of Research of the National Bureau of Standards B 69, 67–72

    MathSciNet  MATH  Google Scholar 

  • Frank, A. [1981]: A weighted matroid intersection algorithm. Journal of Algorithms 2, 328–336

    Article  MathSciNet  MATH  Google Scholar 

  • Frank, A., Tardos, É. [1989]: An application of submodular flows. Linear Algebra and Its Applications 114/115, 329–348

    Article  MathSciNet  Google Scholar 

  • Fulkerson, D.R. [1971]: Blocking and anti-blocking pairs of polyhedra. Mathematical Programming 1, 168–194

    Article  MathSciNet  MATH  Google Scholar 

  • Gabow, H.N. [1995]: A matroid approach to finding edge connectivity and packing arborescences. Journal of Computer and System Sciences 50, 259–273

    Article  MathSciNet  MATH  Google Scholar 

  • Gabow, H.N., Xu, Y. [1996]: Efficient theoretic and practical algorithms for linear matroid intersection problems. Journal of Computer and System Sciences 53, 129–147

    Article  MathSciNet  MATH  Google Scholar 

  • Hausmann, D., Jenkyns, T.A., Korte, B. [1980]: Worst case analysis of greedy type algorithms for independence systems. Mathematical Programming Study 12, 120–131

    Article  MathSciNet  MATH  Google Scholar 

  • Hausmann, D., Korte, B. [1981]: Algorithmic versus axiomatic definitions of matroids. Mathematical Programming Study 14, 98–111

    Article  MathSciNet  MATH  Google Scholar 

  • Jenkyns, T.A. [1976]: The efficiency of the greedy algorithm. Proceedings of the 7th S-E Conference on Combinatorics, Graph Theory, and Computing, Utilitas Mathematica, Winnipeg, pp. 341–350

    Google Scholar 

  • Korte, B., Hausmann, D. [1978]: An analysis of the greedy algorithm for independence systems. In: Algorithmic Aspects of Combinatorics; Annals of Discrete Mathematics 2 (B. Alspach, P. Hell, D.J. Miller, eds.), North-Holland, Amsterdam, pp. 65–74

    Google Scholar 

  • Korte, B., Monma, C.L. [1979]: Some remarks on a classification of oracle-type algorithms. In: Numerische Methoden bei graphentheoretischen und kombinatorischen Problemen; Band 2 (L. Collatz, G. Meinardus, W. Wetterling, eds.), Birkhäuser, Basel, pp. 195–215

    Google Scholar 

  • Lehman, A. [1979]: On the width-length inequality. Mathematical Programming 17, 403–417

    Article  MathSciNet  MATH  Google Scholar 

  • Nash-Williams, C.S.J.A. [1967]: An application of matroids to graph theory. In: Theory of Graphs; Proceedings of an International Symposium in Rome 1966 (P. Rosenstiehl, ed.), Gordon and Breach, New York, pp. 263–265

    Google Scholar 

  • Rado, R. [1942]: A theorem on independence relations. Quarterly Journal of Math. Oxford 13, 83–89

    Article  MathSciNet  MATH  Google Scholar 

  • Rado, R. [1957]: Note on independence functions. Proceedings of the London Mathematical Society 7, 300–320

    Article  MathSciNet  MATH  Google Scholar 

  • Seymour, P.D. [1977]: The matroids with the Max-Flow Min-Cut property. Journal of Combinatorial Theory B 23, 189–222

    Article  MathSciNet  MATH  Google Scholar 

  • Whitney, H. [1933]: Planar graphs. Fundamenta Mathematicae 21, 73–84

    Google Scholar 

  • Whitney, H. [1935]: On the abstract properties of linear dependence. American Journal of Mathematics 57, 509–533

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Discrete Mathematics, University of Bonn, Germany

    Bernhard Korte & Jens Vygen

Authors
  1. Bernhard Korte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens Vygen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Italia

About this chapter

Cite this chapter

Korte, B., Vygen, J. (2011). Matroidi. In: Ottimizzazione Combinatoria. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-1523-4_13

Download citation

Publish with us

Policies and ethics

Search

Navigation