The expressive power of binary submodular functions

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

Volumn 5734 LNCS, Issue , 2009, Pages 744-757

  Živný, Stanislav ^a   Cohen, David A ^b   Jeavons, Peter G ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Decomposition of submodular functions; Min Cut; Pseudo Boolean optimisation; Submodular function minimisation

Indexed keywords

ALGEBRAIC PROPERTIES; EXPRESSIBILITY; EXPRESSIVE POWER; MIN-CUT; OPTIMISATIONS; PSEUDO-BOOLEAN; PSEUDO-BOOLEAN OPTIMISATION; SUBMODULAR; SUBMODULAR FUNCTION MINIMISATION; SUBMODULAR FUNCTIONS;

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTER VISION; FUNCTION EVALUATION; OPTIMIZATION;

BOOLEAN FUNCTIONS;

EID: 70349306522     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-03816-7_63     Document Type: Conference Paper

References (35)

1. Billionet, A., Minoux, M.: Maximizing a supermodular pseudo-Boolean function: a polynomial algorithm for cubic functions. Discrete Applied Math. 12, 1-11 (1985)
2. Boros, E., Hammer, P.L.: Pseudo-Boolean optimization. Discrete Applied Mathematics 123(1-3), 155-225 (2002)
3. Burkard, R., Klinz, B., Rudolf, R.: Perspectives of Monge properties in optimization. Discrete Applied Mathematics 70, 95-161 (1996)
4. Cohen, D., Cooper, M., Jeavons, P.: An algebraic characterisation of complexity for valued constraints. In: Benhamou, F. (ed.) CP 2006. LNCS, vol.4204, pp. 107-121. Springer, Heidelberg (2006)
5. Cohen, D., Cooper, M., Jeavons, P., Krokhin, A.: A maximal tractable class of soft constraints. Journal of Artificial Intelligence Research 22, 1-22 (2004)
6. Cohen, D., Cooper, M., Jeavons, P., Krokhin, A.: Supermodular functions and the complexity of Max-CSP. Discrete Applied Mathematics 149, 53-72 (2005)
7. Cohen, D., Cooper, M., Jeavons, P., Krokhin, A.: The complexity of soft constraint satisfaction. Artificial Intelligence 170, 983-1016 (2006)
8. Cooper, M.: Minimization of Locally Defined Submodular Functions by Optimal Soft Arc Consistency. Constraints 13(4), 437-458 (2008)
9. Crama, Y.: Recognition problems for special classes of polynomials in 0-1 variables. Mathematical Programming 44, 139-155 (1989)
10. Creignou, N., Khanna, S., Sudan, M.: Complexity Classification of Boolean Constraint Satisfaction Problems. SIAM, Philadelphia (2001)
11. Deineko, V., Jonsson, P., Klasson, M., Krokhin, A.: The approximability of Max CSP with fixed-value constraints. Journal of the ACM 55(4) (2008)
12. Feige, U., Mirrokni, V.S., Vondrák, J.: Maximizing non-monotone submodular functions. In: Proceedings of FOCS 2007 (2007)
13. Fisher, M., Nemhauser, G., Wolsey, L.: An analysis of approximations for maximizing submodular set functions-I. Mathematical Programming 14, 265-294 (1978)
14. Fujishige, S.: Submodular Functions and Optimization, 2nd edn. Annals of Discrete Mathematics, vol.58. North-Holland, Amsterdam (2005)
15. Gallo, G., Simeone, B.: On the supermodular knapsack problem. Mathematical Programming 45, 295-309 (1988)
16. Hammer, P.L.: Some network flow problems solved with pseudo-Boolean programming. Operations Research 13, 388-399 (1965)
17. Iwata, S.: Submodular function minimization. Mathematical Programming 112, 45-64 (2008) 10.
18. Jeavons, P., Cohen, D., Cooper, M.: Constraints, consistency and closure. Artificial Intelligence 101(1-2), 251-265 (1998)
19. Jonsson, P., Klasson, M., Krokhin, A.: The approximability of three-valued MAX CSP. SIAM Journal on Computing 35(6), 1329-1349 (2006)
20. Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? IEEE Transactions on PAMI 26(2), 147-159 (2004)
21. Korte, B., Vygen, J.: Combinatorial Optimization, 4th edn. Algorithms and Combinatorics, vol.21. Springer, Heidelberg (2007)
22. Krokhin, A., Larose, B.: Maximizing supermodular functions on product lattices, with application to maximum constraint satisfaction. SIAM Journal on Discrete Mathematics 22(1), 312-328 (2008)
23. Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)
24. Lovász, L.: Submodular functions and convexity. In: Bachem, A., Gr̈otschel, M., Korte, B. (eds.) Math. Programming, pp. 235-257. Springer, Berlin (1983)
25. Motzkin, T., Raiffa, H., Thompson, G., Thrall, R.: The double description method. Contributions to the Theory of Games, vol.2, pp. 51-73. Princeton Univ. Press, Princeton (1953)
26. Narayanan, H.: Submodular Functions and Electrical Networks (1997)
27. Nemhauser, G., Wolsey, L.: Integer and Combinatorial Optimization (1988)
28. Orlin, J.B.: A faster strongly polynomial time algorithm for submodular function minimization. Mathematical Programming 118, 237-251 (2009)
29. Promislow, S., Young, V.: Supermodular functions on finite lattices. Order 22(4), 389-413 (2005)
30. Rhys, J.: A selection problem of shared fixed costs and network flows. Management Science 17(3), 200-207 (1970)
31. Rossi, F., van Beek, P., Walsh, T.: The Handbook of Constraint Programming (2006)
32. Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Algorithms and Combinatorics, vol.24. Springer, Heidelberg (2003)
33. Topkis, D.: Supermodularity and Complementarity (1998)
34. Zalesky, B.: Efficient determination of Gibbs estimators with submodular energy functions. arXiv:math/0304041v1 (February 2008)?
35. Zivny, S., Jeavons, P.G.: Classes of submodular constraints expressible by graph cuts. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol.5202, pp. 112-127. Springer, Heidelberg (2008)