Improved algorithms for submodular function minimization and submodular flow

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2000, Pages 107-116

  Fleischer, Lisa ^a   Iwata, Satoru ^b  

^a Department of Applied Physics and Applied Mathematics   (United States)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL ALGORITHM; COMMON STRUCTURES; DUAL SOLUTIONS; POLYNOMIAL-TIME ALGORITHMS; STRONGLY POLYNOMIALS; SUBMODULAR FLOW; SUBMODULAR FUNCTION MINIMIZATION; TIME COMPLEXITY;

COMPUTATION THEORY; DESIGN; OPTIMIZATION; COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; FUNCTIONS; POLYNOMIALS;

ALGORITHMS;

POLYNOMIAL-TIME ALGORITHMS; SCHRIJVER ALGORITHMS; SUBMODULAR FUNCTIONS;

EID: 0033702895     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/335305.335318     Document Type: Conference Paper

References (16)

1. W. H. Cunningham. Testing membership in matroid polyhedra. J. Combinatorial Theory B, 36:161-188, 1984.
2. W. H. Cunningham. On submodular function minimization. Combinatorica, 5:185-192, 1985.
3. J. Edmonds. Submodular functions, matroids, and certain polyhedra. In R. Guy, H. Hanani, N. Sauer, and J. Schönheim, editors, Combinatorial Structures and their Applications, pages 69-87. Gordon and Breach, 1970.
4. J. Edmonds and R. Giles. A min-max relation for submodular functions on graphs. Ann. Discrete Math., 1:185-204, 1977.
5. L. Fleischer, S, Iwata, and S. T. McCormick. A faster capacity scaling algorithm for submodular flow. Technical Report 9947, C.O.R.E. Discussion Paper, Louvain-la-Neuve, Belgium, 1999.
6. A. Frank. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory, 36:221-239, 1984.
7. A. Frank and É. Tardos. An application of submodular flows. Linear algebra and its applications, 114/115:329-348, 1989.
8. S. Fujishige, H. Röck, and U. Zimmermann. A strongly polynomial algorithm for minimum cost submodular flow problems. Math. Oper. Res., 14:60-69, 1989.
9. S. Fujishige and X. Zhang. New algorithms for the intersection problem of submodular systems. Japan J. Indust. Appl. Math., 9:369-382, 1992.
10. A. V. Goldberg and R. E. Tarjan. A new approach to the maximum flow problem. Journal of the ACM, 35:921-940, 1988.
11. M. Grotschel, L. Lovasz, and A, Schrijver. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica, 1:169-197, 1981.
12. S. Iwata, L. Fleischer, and S. Fujishige. A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions. In Proceedings of the 32th Annual ACM Symposium on Theory of Computing, 2000. This proceedings.
13. S. Iwata, S. T. McCormick, and M. Shigeno. A fast cost scaling algorithm for submodular flow. To appear.
14. T. Jordán. Edge-splitting problems with demands. In G. Cornuéjols, R. E. Burkard, and G. J. Woeginger, editors, Integer Programming and Combinatorial Optimization, volume 1610 of LNCS, pages 273-288, Graz, Austria, June 1999. Springer.
15. M. Queyranne. Minimizing symmetric submodular functions. Math. Programming, 82:3-12, 1998. (Pubitemid 128401579)
16. A. Schrijver. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Preprint. Submitted to JCTB., 1999.