Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
General Literature
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, 1995
Björner, A., and Ziegler, G.M. [1992]: Introduction to greedoids. In: Matroid Applications (N. White, ed.), Cambridge University Press, Cambridge 1992
Fujishige, S. [1991]: Submodular Functions and Optimization. North-Holland, Amsterdam 1991
Korte, B., Lovász, L., and Schrader, R. [1991]: Greedoids. Springer, Berlin 1991
McCormick, S.T. [2004]: Submodular function minimization. In: Handbook on Discrete Optimization (K. Aardal, G. Nemhauser, R. Weismantel, eds.), Elsevier, Berlin (forthcoming)
Schrijver, A. [2003]: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Berlin 2003, Chapters 44-49
Cited References
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. 69–87
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. 39–49
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. 185–204
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), 107–116
Frank, A. [1981]: A weighted matroid intersection algorithm. Journal of Algorithms 2 (1981), 328–336
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. 97–120
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), 626–628
Fujishige, S., Röck, H., and Zimmermann, U. [1989]: A strongly polynomial algorithm for minimum cost submodular flow problems. Mathematics of Operations Research 14 (1989), 60–69
Grötschel, M., Lovász, L., and Schrijver, A. [1981]: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1 (1981), 169–197
Grötschel, M., Lovász, L., and Schrijver, A. [1988]: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin 1988
Iwata, S. [2002]: A fully combinatorial algorithm for submodular function minimization. Journal of Combinatorial Theory B 84 (2002), 203–212
Iwata, S. [2003]: A faster scaling algorithm for minimizing submodular functions. SIAM Journal on Computing 32 (2003), 833–840
Iwata, S., Fleischer, L., L., and Fujishige, S. [2001]: A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions. Journal of the ACM 48 (2001), 761–777
Jensen, P.M., and Korte, B. [1982]: Complexity of matroid property algorithms. SIAM Journal on Computing 11 (1982), 184–190
Lovász, L. [1980]: Matroid matching and some applications. Journal of Combinatorial Theory B 28 (1980), 208–236
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, 495–517
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 1983
Nagamochi, H., and Ibaraki, T. [1998]: A note on minimizing submodular functions. Information Processing Letters 67 (1998), 239–244
Queyranne, M. [1998]: Minimizing symmetric submodular functions. Mathematical Programming B 82 (1998), 3–12
Rizzi, R. [2000]: On minimizing symmetric set functions. Combinatorica 20 (2000), 445–450
Schrijver, A. [2000]: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory B 80 (2000), 346–355
Vygen, J. [2003]: A note on Schrijver’s submodular function minimization algorithm. Journal of Combinatorial Theory B 88 (2003), 399–402
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2006). Generalizations of Matroids. In: Combinatorial Optimization. Algorithms and Combinatorics 21, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29297-7_14
Download citation
DOI: https://doi.org/10.1007/3-540-29297-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25684-7
Online ISBN: 978-3-540-29297-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)