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Generalizations of Matroids

Part of the Algorithms and Combinatorics 21 book series (AC, volume 21)

Keywords

Greedy Algorithm Vertex Cover Submodular Function Incidence Vector Optimum Dual Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

General Literature

  1. Bixby, R.E., and Cunningham, W.H. [1995]: Matroid optimization and algorithms. In: Handbook of Combinatorics; Vol. 1 (R.L. Graham, M. Grötschel, L. Lovász, eds.), Elsevier, Amsterdam, 1995Google Scholar
  2. Björner, A., and Ziegler, G.M. [1992]: Introduction to greedoids. In: Matroid Applications (N. White, ed.), Cambridge University Press, Cambridge 1992Google Scholar
  3. Fujishige, S. [1991]: Submodular Functions and Optimization. North-Holland, Amsterdam 1991MATHGoogle Scholar
  4. Korte, B., Lovász, L., and Schrader, R. [1991]: Greedoids. Springer, Berlin 1991MATHGoogle Scholar
  5. McCormick, S.T. [2004]: Submodular function minimization. In: Handbook on Discrete Optimization (K. Aardal, G. Nemhauser, R. Weismantel, eds.), Elsevier, Berlin (forthcoming)Google Scholar
  6. Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 44-49MATHGoogle Scholar

Cited References

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  2. 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 1979, pp. 39–49Google Scholar
  3. Edmonds, J., and Giles, R. [1977]: A min-max relation for submodular functions on graphs. In: Studies in Integer Programming; Annals of Discrete Mathematics 1 (P.L. Hammer, E.L. Johnson, B.H. Korte, G.L. Nemhauser, eds.), North-Holland, Amsterdam 1977, pp. 185–204Google Scholar
  4. Fleischer, L., and Iwata, S. [2000]: Improved algorithms for submodular function minimization and submodular flow. Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing (2000), 107–116Google Scholar
  5. Frank, A. [1981]: A weighted matroid intersection algorithm. Journal of Algorithms 2 (1981), 328–336CrossRefMathSciNetMATHGoogle Scholar
  6. Frank, A. [1982]: An algorithm for submodular functions on graphs. In: Bonn Workshop on Combinatorial Optimization; Annals of Discrete Mathematics 16 (A. Bachem, M. Grötschel, B. Korte, eds.), North-Holland, Amsterdam 1982, pp. 97–120Google Scholar
  7. Fujishige, S. [1998]: Another simple proof of the validity of Nagamochi and Ibaraki’s min-cut algorithm and Queyranne’s extension to symmetric submodular function minimization. Journal of the Operations Research Society of Japan 41 (1998), 626–628MathSciNetMATHGoogle Scholar
  8. Fujishige, S., Röck, H., and Zimmermann, U. [1989]: A strongly polynomial algorithm for minimum cost submodular flow problems. Mathematics of Operations Research 14 (1989), 60–69MathSciNetCrossRefMATHGoogle Scholar
  9. Grötschel, M., Lovász, L., and Schrijver, A. [1981]: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1 (1981), 169–197MathSciNetMATHGoogle Scholar
  10. Grötschel, M., Lovász, L., and Schrijver, A. [1988]: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin 1988MATHGoogle Scholar
  11. Iwata, S. [2002]: A fully combinatorial algorithm for submodular function minimization. Journal of Combinatorial Theory B 84 (2002), 203–212MathSciNetMATHGoogle Scholar
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  16. Lovász, L. [1981]: The matroid matching problem. In: Algebraic Methods in Graph Theory; Vol. II (L. Lovász, V.T. Sós, eds.), North-Holland, Amsterdam 1981, 495–517Google Scholar
  17. Lovász, L. [1983]: Submodular functions and convexity. In: Mathematical Programming: The State of the Art-Bonn 1982 (A. Bachem, M. Grötschel, B. Korte, eds.), Springer, Berlin 1983Google Scholar
  18. Nagamochi, H., and Ibaraki, T. [1998]: A note on minimizing submodular functions. Information Processing Letters 67 (1998), 239–244CrossRefMathSciNetGoogle Scholar
  19. Queyranne, M. [1998]: Minimizing symmetric submodular functions. Mathematical Programming B 82 (1998), 3–12MathSciNetMATHGoogle Scholar
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