A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2000, Pages 97-106

  Iwata, Satoru ^a   Fleischer, Lisa ^b   Fujishige, Satoru ^a  

^a OSAKA UNIVERSITY   (Japan)

^b Fu Foundation School of Engineering and Applied Science   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION VALUES; POLYNOMIAL-TIME; POLYNOMIAL-TIME ALGORITHMS; SCALING SCHEMES; SUBMODULAR FUNCTIONS;

COMPUTATION THEORY; POLYNOMIALS; COMBINATORIAL MATHEMATICS; FUNCTIONS;

ALGORITHMS;

POLYNOMIAL-TIME ALGORITHMS; SUBMODULAR FUNCTIONS;

EID: 0033706889     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/335305.335317     Document Type: Conference Paper

References (32)

1. R. E. Bixby, W. H. Cunningham, and D. M. Topkis: Partial order of a polymatroid extreme point, Math. Oper. Res., 10 (1985), 367-378.
2. W. H. Cunningham: Testing membership in matroid polyhedra, J. Combinatorial Theory, B36 (1984), 161-188.
3. W. H. Cunningham: On submodular function minimization, Combinatorica, 5 (1985), 185-192.
4. J. Edmonds: Submodular functions, matroids, and certain polyhedra, Combinatorial Structures and Their Applications, R. Guy, H. Hanani, N. Sauer, and J. Schönheim, eds., Gordon and Breach, 69-87, 1970.
5. J. Edmonds and R. Giles: A min-max relation for submodular function on graphs, Ann. Discrete Math., 1 (1977), 185-204.
6. J. Edmonds and R. Karp: Theoretical improvements in algorithmic efficiency for network flow problems, J. ACM, 19 (1972), 248-264.
7. L. Fleischer, S. Iwata, and S. T. McCormick: A faster capacity scaling algorithm for submodular flow, 1999.
8. A. Frank: An algorithm for submodular functions on graphs, Ann. Discrete Math., 16 (1982), 189-212.
9. A. Frank and É. Tardos: An application of simultaneous Diophantine approximation in combinatorial optimization, Combinatorica, 7 (1987), 49-65.
10. A. Frank and É. Tardos: Generalized polymatroids and submodular flows, Math. Programming, 42 (1988), 489-563.
11. S. Fujishige: Polymatroidal dependence structure of a set of random variables, Information and Control, 39 (1978), 55-72.
12. S. Fujishige: Lexicographically optimal base of a polymatroid with respect to a weight vector, Math. Oper. Res., 5 (1980), 186-196.
13. S. Fujishige: Submodular systems and related topics, Math. Programming Study, 22 (1984), 113-131.
14. S. Fujishige: Theory of submodular programs: A Fenchel-type min-max theorem and subgradients of submodular functions, Math. Programming, 29 (1984), 142-155.
15. S. Fujishige: Submodular Functions and Optimization, North-Holland, 1991.
16. M. X. Goemans and V. S. Ramakrishnan: Minimizing submodular functions over families of subsets, Combinatorica, 15 (1995), 499-513.
17. M. Grötschel, L. Lovász, and A. Schrijver: The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), 169-197.
18. M. Grötschel, L. Lovász, and A. Schrijver: Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, 1988.
19. T.-S. Han: The capacity region of general multiple-access channel with correlated sources, Information and Control, 40 (1979), 37-60.
20. B. Hoppe and É. Tardos: The quickest transshipment problem, Proceedings of Fifth ACM/SIAM Symposium on Discrete Algorithms (1995), 512-521.
21. H. Ito, S. Iwata, and K. Murota: Block-triangularization of partitioned matrices under similarity/equivalence transformations, SIAM J. Matrix Anal. Appl., 15 (1994), 1226-1255.
22. S. Iwata: A capacity scaling algorithm for convex cost submodular flows, Math. Programming, 76 (1997), 299-308.
23. S. Iwata, S. T. McCormick, and M. Shigeno: A strongly polynomial cut canceling algorithm for the submodular flow problem, Proceedings of the Seventh MPS Conference on Integer Programming and Combinatorial Optimization (1999), 259-272.
24. S. Iwata and K. Murota: A minimax theorem and a Dulmage-Mendelsohn type decomposition for a class of generic partitioned matrices, SIAM J. Matrix Anal. Appl., 16 (1995), 719-734.
25. L. Lovász: Submodular functions and convexity. Mathematical Programming - The State of the Art, A. Bachem, M. Grötschel and B. Korte, eds., Springer-Verlag, 1983, 235-257.
26. H. Nagamochi and T. Ibaraki: Computing edge-connectivity in multigraphs and capacitated graphs, SIAM J. Discrete Math., 5 (1992), 54-64.
27. H. Narayanan: A rounding technique for the polymatroid membership problem, Linear Algebra Appl., 221 (1995), 41-57.
28. M. Queyranne: Minimizing symmetric submodular functions, Math. Programming, 82 (1998), 3-12.
29. A. Schrijver: A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combinatorial Theory, Ser. B, submitted.
30. M. A. Sohoni: Membership in submodular and other polyhedra. Technical Report TR-102-92, Department of Computer Science and Engineering, Indian Institute of Technology, Bombay, India, 1992.
31. A. Tamir: A unifying location model on tree graphs based on submodularity properties, Discrete Appl. Math., 47 (1993), 275-283.
32. É. Tardos: A strongly polynomial minimum cost circulation algorithm, Combinatorica, 5 (1985), 247-255.