Size-constrained submodular minimization through minimum norm base

Proceedings of the 28th International Conference on Machine Learning, ICML 2011

Volumn , Issue , 2011, Pages 977-984

  Nagano, Kiyohito ^a   Kawahara, Yoshinobu ^b   Aihara, Kazuyuki ^a  

^a INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL OPTIMIZATION PROBLEMS; COMPUTATIONAL EXPERIMENT; DENSEST SUBGRAPH PROBLEMS; GRAPH PARTITIONING PROBLEMS; MINIMIZATION PROBLEMS; MINIMUM NORM; NP-HARD; NP-HARDNESS; OPTIMAL SOLUTIONS; POLYHEDRAL THEORY; POLYNOMIAL-TIME; SIZE CONSTRAINT; STRONGLY POLYNOMIALS; SUBMODULAR; SUBMODULAR FUNCTIONS;

COMBINATORIAL OPTIMIZATION; CONSTRAINED OPTIMIZATION; LEARNING SYSTEMS; OPTIMAL SYSTEMS; POLYNOMIAL APPROXIMATION;

APPROXIMATION ALGORITHMS;

EID: 80053442724     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. Edmonds, J. Submodular functions, matroids, and certain polyhedra. In Guy, R., Hanani, H., Sauer, N., and Schönheim, J. (eds.), Combinatorial Structures and Their Applications, pp. 69-87. Gordon and Breach, 1970.
2. Feige, U., Kortsarz, G., and Peleg, D. The dense k-subgraph problem. Algorithmica, 29:410-421, 2001. (Pubitemid 33710542)
3. Fleischer, L. and Iwata, S. A push-relabel framework for submodular function minimization and applications to parametric optimization. Discrete Appl. Math., 131:311-322, 2003.
4. Fujishige, S. Lexicographically optimal base of a polymatroid with respect to a weight vector. Mathematics of Operations Research, 5:186-196, 1980.
5. Fujishige, S. Submodular Functions and Optimization. Elsevier, 2nd edition, 2005.
6. Fujishige, S., Hayashi, T., and Isotani, S. The minimum-norm-point algorithm applied to submodular function minimization and linear programming. Technical report, Research Institute for Mathematical Sciences Preprint RIMS-1571, Kyoto University, Kyoto, Japan, 2006.
7. Garey, M. R. and Johnson, D. S. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., 1979.
8. Goel, G., Karande, C., Tripathi, P., and Wang, L. Approximability of combinatorial problems with multi-agent submodular cost functions. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009), pp. 755-764, 2009.
9. Grötschel, M., Lovász, L., and Schrijver, A. Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, 2nd edition, 1988.
10. Iwata, S. and Nagano, K. Submodular function minimization under covering constraints. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009), pp. 671-680, 2009.
11. Iwata, S., Fleischer, L., and Fujishige, S. A combinatorial strongly polynomial algorithm for minimizing submodular functions. Journal of the ACM, 48:761-777, 2001.
12. Krauthgamer, R. and Feige, U. A polylogarithmic approximation of the minimum bisection. SIAM Review, 48:99-130, 2006.
13. Lovász, L. Submodular functions and convexity. In Bachem, A., Grötschel, M., and Korte, B. (eds.), Mathematical Programming - The State of the Art, pp. 235-257. Springer-Verlag, 1983.
14. Nagano, K. A faster parametric submodular function minimization algorithm and applications. Technical report, METR 2007-43, University of Tokyo, Tokyo, Japan, 2007.
15. Nagano, K., Kawahara, Y., and Iwata, S. Minimum average cost clustering. In Advances in Neural Information Processing Systems 23 (NIPS 2010), pp. 1759-1767, 2010.
16. Narasimhan, M., Jojic, N., and Bilmes, J. Q-clustering. In Advances in Neural Information Processing Systems 18 (NIPS 2005), pp. 979-986, 2005.
17. Orlin, J. B. A faster strongly polynomial time algorithm for submodular function minimization. Mathematical Programming, 118:237-251, 2009.
18. Schrijver, A. A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory (B), 80:346-355, 2000.
19. Stobbe, P. and Krause, A. Efficient minimization of decomposable submodular functions. In Advances in Neural Information Processing Systems 23 (NIPS 2010), pp. 2208-2216, 2010.
20. Svitkina, Z. and Fleischer, L. Submodular approximation: sampling-based algorithms and lower bounds. In Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2008), pp. 697-706, 2008.