Submodular function maximization via the multilinear relaxation and contention resolution schemes

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2011, Pages 783-792

  Chekuri, Chandra ^a   Vondrák, Jan ^b   Zenklusen, Rico ^c  

^a University of Illinois at Urbana Champaign   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

approximation algorithm; contention resolution scheme; independence constraint; matroid; submodular function maximization

Indexed keywords

COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION; COMPUTATION THEORY; MATRIX ALGEBRA;

CONSTANT-FACTOR APPROXIMATION ALGORITHMS; CONTENTION RESOLUTION; FRACTIONAL SOLUTIONS; INDEPENDENCE CONSTRAINT; KNAPSACK CONSTRAINTS; MULTILINEAR EXTENSION; SUBMODULAR FUNCTIONS; SUBMODULAR SET FUNCTIONS;

APPROXIMATION ALGORITHMS;

EID: 79959724727     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1993636.1993740     Document Type: Conference Paper

References (42)

1. st ACM-SIAM SODA, 1087-1096, 2010.
2. N. Alon and J. Spencer. The Probabilistic Method. 2nd Edition, John Wiley & Sons, 2000.
3. th IPCO, 369-382, 2010.
4. th IPCO, 439-456, 2001.
5. th IPCO, 182-196, 2007.
6. G. Calinescu, C. Chekuri, M. Pál and J. Vondrák. Maximizing a monotone submodular set function subject to a matroid constraint. To appear in SIAM J. on Computing special issue for ACM STOC 2008.
7. A. Chakrabarti, C. Chekuri, A. Gupta and A. Kumar. Approximation algorithms for the unsplittable flow problem. Algorithmica, 47(1):53-78, 2007. (Pubitemid 46220348)
8. T. Chan and S. Har-Peled. Approximation algorithms for maximum independent set of pseudo-disks. Full version of a paper that appeared in Proc. of ACM SoCG, 2009. Available at http://arxiv.org/abs/1103.1431.
9. S. Chawla, J. Hartline, D. Malec and B. Sivan. Sequential posted pricing and multi-parameter mechanism design. Manuscript, 2009, available at http://arxiv.org/abs/0907.2435v1.
10. nd ACM STOC, 311-320, 2010.
11. th APPROX, 42-55, 2009.
12. C. Chekuri, M. Mydlarz and F. B. Shepherd. Multicommodity demand flow in a tree and packing integer programs. ACM Trans. on Algorithms, to appear.
13. Preliminary version in Proc. of ICALP, 410-425, 2003.
14. st IEEE FOCS, 575-584, 2010.
15. G. Cornuejols, M. L. Fisher and G. Nemhauser. Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms. Management Science, 23:789-810, 1977.
16. U. Feige. A threshold of ln n for approximating set cover. Journal of the ACM, 45(4):634-652, 1998. (Pubitemid 128488790)
17. th IEEE FOCS, 461-471, 2007.
18. U. Feige and J. Vondrák. Approximation algorithms for allocation problems: Improving the factor of 1 - 1/e. Proc. of 47th IEEE FOCS, 667-676, 2006. (Pubitemid 351175554)
19. M. L. Fisher, G. L. Nemhauser and L. A. Wolsey. An analysis of approximations for maximizing submodular set functions - II. Math. Prog. Study, 8:73-87, 1978.
20. th ICALP, 262-274, 2010. A more detailed version available at http://arxiv.org/abs/1003.0722.
21. A. Gupta, A. Roth, G. Schoenebeck and K. Talwar. Constrained non-monotone submodular maximization: Offline and secretary algorithms. CoRR, abs/1003.1517, 2010.
22. S. G. Kolliopoulos and C. Stein. Approximating disjoint-path problems using greedy algorithms and Packing Integer Programs. Math. Programming A, (99):63-87, 2004.
23. Preliminary version in Proc. of IPCO, 1998.
24. th ACM-SIAM SODA, 545-554, 2009.
25. A. Kulik, H. Shachnai and T. Tamir. Approximations for monotone and non-monotone submodular maximization with knapsack constraints. Manuscript, 2010.
26. J. Lee, V. Mirrokni, V. Nagarajan and M. Sviridenko. Maximizing nonmonotone submodular functions under matroid and knapsack constraints. SIAM J. on Disc. Math., 23(4): 2053-2078, 2010.
27. st ACM STOC, 323-332, 2009.
28. th APPROX, 244-257, 2009.
29. th ACM STOC, 369-378, 2010.
30. th ACM EC, 70-77, 2008.
31. G. L. Nemhauser and L. A. Wolsey. Best algorithms for approximating the maximum of a submodular set function. Math. Oper. Research, 3(3):177-188, 1978.
32. G. L. Nemhauser, L. A. Wolsey and M. L. Fisher. An analysis of approximations for maximizing submodular set functions - I. Math. Prog., 14:265-294, 1978.
33. nd ACM-SIAM SODA, 1098-1116, 2011.
34. A. Schrijver. Combinatorial Optimization - Polyhedra and Efficiency. Springer, 2003.
35. th ACM-SIAM SODA, 567-576, 2001.
36. M. Sviridenko. A note on maximizing a submodular set function subject to knapsack constraint. Operations Research Letters 32, 41-43, 2004.
37. L.G. Valiant. The complexity of enumeration and reliability problems. SIAM Journal on Computing 8(3):410-421, 1979.
38. J. Vondrák. Submodularity in combinatorial optimization. PhD Thesis, Charles University, 2007.
39. th ACM STOC, 67-74, 2008.
40. th IEEE FOCS, 251-270, 2009.
41. J. Vondrák. A note on concentration of submodular functions. Manuscript, 2010, available at http://arxiv.org/abs/1005.2791.
42. th ACM-SIAM SODA, 710-719, 2011.