Generalized roof duality and bisubmodular functions

Discrete Applied Mathematics

Volumn 160, Issue 4-5, 2012, Pages 416-426

  Kolmogorov, Vladimir ^a  

^a INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA   (Austria)

Author keywords

Bisubmodularity; Pseudo boolean optimization; Roof duality

Indexed keywords

BISUBMODULARITY; CONCEPTUAL LEVELS; CONVEX RELAXATION; EXTREME POINTS; HIGHER ORDER; MINIMUM CUT; NATURAL GENERALIZATION; PSEUDO-BOOLEAN FUNCTION; PSEUDO-BOOLEAN OPTIMIZATION; SUBMODULAR FUNCTIONS;

INTEGRAL EQUATIONS; RELAXATION PROCESSES; ROOFS;

BOOLEAN FUNCTIONS;

EID: 84856111789     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2011.10.026     Document Type: Article

References (32)

1. Asem M. Ali, Aly A. Farag, Georgy L. Gimel'Farb, Optimizing binary MRFs with higher order cliques, in: ECCV, 2008.
2. Kazutoshi Ando, Satoru Fujishige, and Takeshi Naitoh A characterization of bisubmodular functions Discrete Math. 148 1996 299 303 (Pubitemid 126367382)
3. M.L. Balinski Integer programming: methods, uses, computation Manag. Sci. 12 3 1965 253 313
4. E. Boros, and P.L. Hammer Pseudo-Boolean optimization Discrete Appl. Math. 123 13 2002 155 225
5. E. Boros, P.L. Hammer, X. Sun, Network flows and minimization of quadratic pseudo-Boolean functions, Technical Report RRR 17-1991, RUTCOR, May 1991.
6. E. Boros, P.L. Hammer, G. Tavares, Preprocessing of unconstrained quadratic binary optimization, Technical Report RRR 10-2006, RUTCOR, 2006.
7. A. Bouchet Greedy algorithm and symmetric matroids Math. Program. 38 1987 147 159
8. A. Bouchet, and W.H. Cunningham Delta-matroids, jump systems and bisubmodular polyhedra SIAM J. Discrete Math. 8 1995 17 32
9. Y. Boykov, O. Veksler, and R. Zabih Fast approximate energy minimization via graph cuts Pattern Anal. Mach. Intell. 23 11 2001
10. R. Chandrasekaran, and Santosh N. Kabadi Pseudomatroids Discrete Math. 71 1988 205 217
11. S. Fujishige Submodular Functions and Optimization 1991 North-Holland
12. Satoru Fujishige, and Satoru Iwata Bisubmodular function minimization SIAM J. Discrete Math. 19 4 2006 1065 1073 (Pubitemid 44775303)
13. P.L. Hammer, P. Hansen, and B. Simeone Roof duality, complementation and persistency in quadratic 01 optimization Math. Program. 28 1984 121 155 (Pubitemid 14569633)
14. D. Hochbaum, Instant recognition of half integrality and 2-approximations, in: 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, 1998.
15. D. Hochbaum Solving integer programs over monotone inequalities in three variables: a framework for half integrality and good approximations European J. Oper. Res. 140 2 2002 291 321 (Pubitemid 34435035)
16. H. Ishikawa, Higher-order clique reduction in binary graph cut, in: CVPR, 2009.
17. H. Ishikawa, Higher-order gradient descent by fusion-move graph cut, in: ICCV, 2009.
18. Satoru Iwata, Kiyohito Nagano, Submodular function minimization under covering constraints, in: FOCS, October 2009.
19. Santosh N. Kabadi, and R. Chandrasekaran On totally dual integral systems Discrete Appl. Math. 26 1990 87 104
20. V. Kolmogorov, Minimizing a sum of submodular functions, Technical Report, June 2010. arXiv:1006.1990v1.
21. L-convex and bisubmodular functions, in: 36th International Symposium on Mathematical Foundations of Computer Science, MFCS, August 2011.
22. Victor Lempitsky, Carsten Rother, Andrew Blake, LogCutefficient graph cut optimization for Markov random fields, in: ICCV, 2007.
23. Victor Lempitsky, Carsten Rother, Stefan Roth, and Andrew Blake Fusion moves for Markov random field optimization Pattern Anal. Mach. Intell. 2009
24. S.H. Lu, and A.C. Williams Roof duality for polynomial 01 optimization Math. Program. 37 3 1987 357 360
25. S. Thomas McCormick, and Satoru Fujishige Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimization Math. Program. Ser. A 122 2010 87 120
26. M. Nakamura, A characterization of greedy sets: universal polymatroids (I), in: Scientific Papers of the College of Arts and Sciences, vol. 38 (2). The University of Tokyo, 1998, pp. 155167.
27. G.L. Nemhauser, and L.E. Trotter Vertex packings: structural properties and algorithms Math. Program. 8 1975 232 248
28. Liqun Qi Directed submodularity, ditroids and directed submodular flows Math. Program. 42 1988 579 599
29. A. Raj, G. Singh, R. Zabih, MRF's for MRI's: Bayesian reconstruction of MR images via graph cuts, in: CVPR, 2006.
30. Stefan Roth, and Michael J. Black Fields of experts Int. J. Comput. Vis. 82 2 2009 205 229
31. C. Rother, V. Kolmogorov, V. Lempitsky, M. Szummer, Optimizing binary MRFs via extended roof duality, in: CVPR, June 2007.
32. O. Woodford, P. Torr, I. Reid, A. Fitzgibbon, Global stereo reconstruction under second order smoothness priors, in: CVPR, 2008.