Generalizations of Matroids

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


Greedy Algorithm Vertex Cover Submodular Function Incidence Vector Optimum Dual Solution 
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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 1991zbMATHGoogle Scholar
  4. Korte, B., Lovász, L., and Schrader, R. [1991]: Greedoids. Springer, Berlin 1991zbMATHGoogle 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 44-49zbMATHGoogle Scholar

Cited References

  1. 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. Schonheim, eds.), Gordon and Breach, New York 1970, pp. 69–87Google Scholar
  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), 328–336CrossRefMathSciNetzbMATHGoogle 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), 626–628MathSciNetzbMATHGoogle Scholar
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  11. Iwata, S. [2002]: A fully combinatorial algorithm for submodular function minimization. Journal of Combinatorial Theory B 84 (2002), 203–212MathSciNetzbMATHGoogle 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), 3–12MathSciNetzbMATHGoogle Scholar
  20. Rizzi, R. [2000]: On minimizing symmetric set functions. Combinatorica 20 (2000), 445–450CrossRefMathSciNetzbMATHGoogle Scholar
  21. Schrijver, A. [2000]: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory B 80 (2000), 346–355MathSciNetzbMATHGoogle Scholar
  22. Vygen, J. [2003]: A note on Schrijver’s submodular function minimization algorithm. Journal of Combinatorial Theory B 88 (2003), 399–402MathSciNetzbMATHGoogle Scholar

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