Approximating submodular functions everywhere

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2009, Pages 535-544

  Goemans, Michel X ^a   Harvey, Nicholas J A ^b   Iwata, Satoru ^c   Mirrokni, Vahab ^d  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b MICROSOFT RESEARCH   (United Kingdom)

^c KYOTO UNIVERSITY   (Japan)

^d GOOGLE INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL OPTIMIZATION;

DETERMINISTIC ALGORITHMS; EXACT MINIMIZATION; NON NEGATIVES; POLYMATROIDS; RANK FUNCTIONS; SUBMODULAR FUNCTIONS;

COMBINATORIAL MATHEMATICS;

EID: 70349108343     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973068.59     Document Type: Conference Paper

References (35)

1. N. Alon and J. Spencer. "The Probabilistic Method". Wiley, second edition, 2000.
2. A. Asadpour and A. Saberi. "An approximation algorithm for max-min fair allocation of indivisible goods". STOC, 114-121, 2007.
3. A. Assad and W. Xu. "The Quadratic Minimum Spanning Tree Problem". Naval Research Logistics, 39, 1992.
4. K. Ball. "An Elementary Introduction to Modern Convex Geometry". Flavors of Geometry, MSRI Publications, 1997.
5. R. G. Bland, D. Goldfarb and M. J. Todd. "The Ellipsoid Method: A Survey". Operations Research, 29, 1981.
6. S. Dobzinski and M. Schapira. "An improved approximation algorithm for combinatorial auctions with submodular bidders". SODA, 1064-1073, 2006.
7. J. Edmonds, "Matroids and the Greedy Algorithm", Mathematical Programming, 1, 127-136, 1971.
8. K. Fan, "On a theorem of Weyl concerning the eigenvalues of linear transformations, II", Proc. Nat. Acad. Sci., 1950.
9. U. Feige, V. Mirrokni and J. Vondrak, "Maximizing non-monotone submodular functions", FOCS, 461-471, 2007.
10. S. Fujishige, "Submodular Functions and Optimization", volume 58 of Annals of Discrete Mathematics. Elsevier, second edition, 2005.
11. D. Golovin, "Max-Min Fair Allocation of Indivisible Goods". Technical Report CMU-CS-05-144, 2005.
12. M. Grötschel, L. Lovász, and A. Schrijver, "Geometric Algorithms and Combinatorial Optimization", Springer Verlag, second edition, 1993.
13. O. Güler and F. Gürtina, "The extremal volume ellipsoids of convex bodies, their symmetry properties, and their determination in some special cases", arXiv:0709.707v1.
14. S. Iwata, L. Fleischer, and S. Fujishige, "A combinatorial, strongly polynomial-time algorithm for minimizing submodular functions", Journal of the ACM, 48, 761-777, 2001.
15. S. Iwata and J. Orlin, "A Simple Combinatorial Algorithm for Submodular Function Minimization", SODA, 2009.
16. F. John. "Extremum problems with inequalities as subsidiary conditions", Studies and Essays, presented to R. Courant on his 60th Birthday, January 8, 1948, Interscience, New York, 187-204, 1948.
17. L. G. Khachiyan. "Rounding of polytopes in the real number model of computation", Math of OR, 21, 307-320, 1996. (Pubitemid 126600322)
18. S. Khot, R. Lipton, E. Markakis and A. Mehta. "Inapproximability results for combinatorial auctions with submodular utility functions", WINE, 92-101, 2005.
19. S. Khot and A. Ponnuswami. "Approximation Algorithms for the Max-Min Allocation Problem". APPROXRANDOM, 204-217, 2007.
20. P. Kumar and E. A. Yildirim, "Minimum-Volume Enclosing Ellipsoids and Core Sets", Journal of Optimization Theory and Applications, 126, 1-21, 2005. (Pubitemid 41125931)
21. B. Lehmann, D. J. Lehmann and N. Nisan. "Combinatorial auctions with decreasing marginal utilities", Games and Economic Behavior, 55, 270-296, 2006.
22. J. K. Lenstra, D. B. Shmoys and E. Tardos. "Approximation algorithms for scheduling unrelated parallel machines". Mathematical Programming, 46, 259-271, 1990.
23. L. Lovász, "Submodular Functions and Convexity", in A. Bachern et al., eds, Mathematical Programmming: The State of the Art, 235-257, 1983.
24. J.Matoušek, "Lectures on Discrete Geometry". Springer, 2002.
25. K. Murota, "Discrete Convex Analysis", SIAM Monographs on Discrete Mathematics and Applications, SIAM, 2003.
26. H. Narayanan, "Submodular Functions and Electrical Networks", Elsevier, 1997.
27. G. L. Nemhauser, L. A. Wolsey and M. L. Fisher. "An analysis of approximations for maximizing submodular set functions I". Mathematical Programming, 14, 1978.
28. A. Schrijver, "Combinatorial Optimization: Polyhedra and Efficiency". Springer, 2004.
29. A. Schrijver, "A combinatorial algorithm minimizing submodular functions in strongly polynomial time", Journal of Combinatorial Theory, Series B, 80, 346-355, 2000.
30. J. Spencer, "Six Standard Deviations Suffice", Trans. Amer. Math. Soc., 289, 679-706, 1985.
31. P. Sun and R. M. Freund. "Computation of Minimum Volume Covering Ellipsoids", Operations Research, 52, 690-706, 2004.
32. Z. Svitkina and L. Fleischer. "Submodular Approximation: Sampling-Based Algorithms and Lower Bounds". FOCS, 2008.
33. M. J. Todd. "On Minimum Volume Ellipsoids Containing Part of a Given Ellipsoid". Math of OR, 1982.
34. J. Vondrák. "Optimal Approximation for the Submodular Welfare Problem in the Value Oracle Model". STOC, 2008.
35. L. A. Wolsey. "An Analysis of the Greedy Algorithm for the Submodular Set Covering Problem". Combinatorica, 2, 385-393, 1982.