Bisubmodular function minimization

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2081, Issue , 2001, Pages 160-169

  Fujishige, Satoru ^a   Iwata, Satoru ^b  

^a OSAKA UNIVERSITY   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL OPTIMIZATION; GEOMETRY; INTEGER PROGRAMMING; POLYNOMIAL APPROXIMATION;

POLYNOMIAL-TIME ALGORITHMS; RANK FUNCTIONS; SCALING ALGORITHM; STRONGLY POLYNOMIAL ALGORITHM; SUBMODULAR FUNCTION MINIMIZATION;

COMBINATORIAL MATHEMATICS;

EID: 23044525885     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45535-3_13     Document Type: Conference Paper

References (22)

1. K. Ando and S. Fujishige: On structures of bisubmodular polyhedra, Math. Programming, 74 (1996), 293-317.
2. E. Balas and W. R. Pulleyblank: The perfectly matchable subgraph polytope of an arbitrary graph, Combinatorica, 9 (1989), 321-337.
3. A. Bouchet: Greedy algorithm and symmetric matroids, Math. Programming,38 (1987), 147-159.
4. A. Bouchet: Matchings and A-matroids, Discrete Appi. Math., 24 (1989), 55-62.
5. A. Bouchet and W. H. Cunningham: Delta-matroids, jump systems and bisubmodular polyhedra, SIAM J. Discrete Math., 8 (1995), 17-32.
6. R. Chandrasekaran and S. N. Kabadi: Pseudomatroids, Discrete Math., 71 (1988), 205-217.
7. W. H. Cunningham: Testing membership in matroid polyhedra, J. Combin. Theory, B36 (1984), 161-188.
8. W. H. Cunningham: On submodular function minimization, Combinatorica,5 (1985), 185-192.
9. W. H. Cunningham and J. Green-Krotki: b-matching degree sequence polyhedra, Combinatorica, 11 (1991), 219-230.
10. W. H. Cunningham and J. Green-Krotki: A separation algorithm for the matchable set polytope, Math. Programming, 65 (1994), 139-150.
11. A. Dress and T. F. Havel: Some combinatorial properties of discriminants in metric vector spaces, Adv. Math., 62 (1986), 285-312.
12. F. D. J. Dunstan and D. J. A. Welsh: A greedy algorithm solving a certain class of linear programmes, Math. Programming, 5 (1973), 338-353.
13. A. Frank and E. Tardos: An application of simultaneous Diophantine approximation in combinatorial optimization, Combinatorica, 7 (1987), 49-65.
14. S. Fujishige: Submodular Functions and Optimization, North-Holland, 1991.
15. S. Fujishige: A min-max theorem for bisubmodular polyhedra, SIAM J. Discrete Math., 10 (1997), 294-308.
16. M. Grotschel, L. Lovasz, and A. Schrijver: The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1 (1981), 169-197.
17. M. Grotschel, L. Lovasz, and A. Schrijver: Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, 1988.
18. S. Iwata, L. Fleischer, and S. Fujishige: A combinatorial strongly polynomial algorithm for minimizing submodular functions, J. ACM, to appear.
19. L. Lovasz: Submodular functions and convexity. Mathematical Programming — The State of the Art, A. Bachem, M. Grotschel and B. Korte, eds., Springer-Verlag, 1983, 235-257.
20. L. Lovasz: The membership problem in jump systems, J. Combin. Theory, Ser. B, 70 (1997), 45-66.
21. L. Qi: Directed submodularity, ditroids and directed submodular flows, Math. Programming, 42 (1988), 579-599.
22. A. Schrijver: A combinatorial algorithm minimizing submodular functions in strongly polynomial time, J. Combin. Theory, Ser. B, 80 (2000), 346-355.