A push-relabel framework for submodular function minimization and applications to parametric optimization

Discrete Applied Mathematics

Volumn 131, Issue 2, 2003, Pages 311-322

  Fleischer, Lisa ^a   Iwata, Satoru ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Parametric optimization; Submodular function

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; MATHEMATICAL MODELS; OPTIMIZATION; POLYNOMIALS; SET THEORY;

SUBMODULAR THEORY;

FUNCTIONS;

EID: 0041828774     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(02)00458-4     Document Type: Conference Paper

References (19)

1. Cunningham W.H. Testing membership in matroid polyhedra. J. Combin. Theory B. 36:1984;161-188.
2. Cunningham W.H. On submodular function minimization. Combinatorica. 5:1985;185-192.
3. Dinkelbach W. On nonlinear fractional programming. Management Sci. 13:1967;492-498.
4. Edmonds J. Submodular functions, matroids, and certain polyhedra. Guy R., Hanani H., Sauer N., Schönheim J. Combinatorial Structures and their Applications. 1970;69-87 Gordon and Breach, London.
5. Fleischer L., Iwata S., McCormick S.T. A faster capacity scaling algorithm for submodular flow. Math. Programming. 92:2002;119-139.
6. Fujishige S. Lexicographically optimal base of a polymatroid with respect to a weight vector. Math. Oper. Res. 5:1980;186-196.
7. Fujishige S., Zhang X. New algorithms for the intersection problem of submodular systems. Japan J. Ind. Appl. Math. 9:1992;369-382.
8. Gallo G., Grigoriadis M.D., Tarjan R.E. A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18:1989;30-55.
9. Goldberg A.V., Tarjan R.E. A new approach to the maximum flow problem. J. ACM. 35:1988;921-940.
10. Grötschel M., Lovász L., Schrijver A. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica. 1:1981;169-197.
11. Grötschel M., Lovász L., Schrijver A. Geom. Algorithms and Combin. Optimization. 1988;Springer, Berlin.
12. Iwata S. A capacity scaling algorithm for convex cost submodular flows. Math. Programming. 76:1997;299-308.
13. Iwata S., Fleischer L., Fujishige S. A combinatorial strongly polynomial algorithm for minimizing submodular functions. J. ACM. 48:2001;761-777.
14. S. Iwata, S.T. McCormick, M. Shigeno, A strongly polynomial cut canceling algorithm for the submodular flow problem, in: Proceedings of the 7th Conference on Integer Programming and Combinatorial Optimization (IPCO), Graz, Austria, 1999, pp. 259-272.
15. Iwata S., Murota K., Shigeno M. A fast parametric submodular intersection algorithm for strong map sequences. Math. Oper. Res. 22:1997;803-813.
16. Megiddo N. Optimal flows in networks with multiple sources and sinks. Math. Programming. 7:1974;97-107.
17. Schrijver A. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. J. Combin. Theory B. 80:2000;346-355.
18. Tardos É., Tovey C.A., Trick M.A. Layered augmenting path algorithms. Math. Oper. Res. 11:1986;362-370.
19. Topkis D.M. Minimizing a submodular function on a lattice. Oper. Res. 26:1978;305-321.