A strongly polynomial algorithm for line search in submodular polyhedra

Discrete Optimization

Volumn 4, Issue 3-4, 2007, Pages 349-359

  Nagano, Kiyohito ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Exchange capacity; Network flow; Submodular function

Indexed keywords

ALGORITHMS; FUNCTIONAL ANALYSIS; NUMERICAL METHODS; PARAMETER ESTIMATION;

EXCHANGE CAPACITY; NETWORK FLOW; SUBMODULAR FUNCTION; SUBMODULAR POLYHEDRA;

POLYNOMIALS;

EID: 36448961230     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2007.09.002     Document Type: Article

References (22)

1. Ahuja R.K., Magnanti T.L., and Orlin J.B. Network Flows-Theory, Algorithms, and Applications (1993), Prentice-Hall, Englewood, NJ
2. Bixby R.E., Cunningham W.H., and Topkis D.M. The partial order of a polymatroid extreme point. Mathematics of Operations Research 10 (1985) 367-378
3. Cunningham W.H. Minimum cuts, modular functions, and matroid polyhedra. Networks 15 (1985) 205-215
4. Edmonds J. Submodular functions, matroids, and certain polyhedra. In: Guy R., Hanai H., Sauer N., and Schönheim J. (Eds). Combinatorial Structures and Their Applications (1970), Gordon and Breach, New York 69-87
5. Fleischer L., and Iwata S. A push-relabel framework for submodular function minimization and applications to parametric optimization. Discrete Applied Mathematics 131 (2003) 311-322
6. Fujishige S. Lexicographically optimal base of a polymatroid with respect to a weight vector. Mathematics of Operations Research 5 (1980) 186-196
7. Fujishige S. Submodular Functions and Optimization (1991), North-Holland, Amsterdam
8. Gale D. A theorem on flows in networks. Pacific Journal of Mathematics 7 (1957) 1073-1082
9. Hartvigsen D. A submodular optimization problem with side constraints. Mathematics of Operations Research 23 (1998) 661-679
10. Hartvigsen D. A strongly polynomial time algorithm for a constrained submodular optimization problem. Discrete Applied Mathematics 113 (2001) 183-194
11. Iwata S. A fully combinatorial algorithm for submodular function minimization. Journal of Combinatorial Theory (B) 84 (2002) 203-212
12. Iwata S. A faster scaling algorithm for minimizing submodular functions. SIAM Journal on Computing 32 (2003) 833-840
13. Iwata S., Fleischer L., and Fujishige S. A combinatorial strongly polynomial algorithm for minimizing submodular functions. Journal of the ACM 48 (2001) 761-777
14. Megiddo N. Optimal flows in networks with multiple sources and sinks. Mathematical Programming 7 (1974) 97-107
15. Megiddo N. Combinatorial optimization with rational objective functions. Mathematics of Operations Research 4 (1979) 414-424
16. Megiddo N. Applying parallel computation algorithms in the design of serial algorithms. Journal of the ACM 30 (1983) 852-865
17. Murota K. Discrete Convex Analysis (2003), Society for Industrial and Applied Mathematics, Philadelphia
18. Picard J.C. Maximal closure of a graph and applications to combinatorial problems. Management Science 22 (1976) 1268-1272
19. Radzik T. Parametric flows, weighted means of cuts, and fractional combinatorial optimization. In: Pardalos P.M. (Ed). Complexity in Numerical Optimization (1993), World Scientific, Singapore 351-386
20. Radzik T. Fractional combinatorial optimization. In: Du D.Z., and Pardalos P.M. (Eds). Handbook of Combinatorial Optimization vol. 1 (1998), Kluwer Academic Publishers, Boston 429-478
21. Schrijver A. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory (B) 80 (2000) 346-355
22. Vygen J. A note on Schrijver's submodular function minimization algorithm. Journal of Combinatorial Theory (B) 88 (2003) 399-402