Maximizing a submodular set function subject to a matroid constraint

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

Volumn 4513 LNCS, Issue , 2007, Pages 182-196

  Calinescu, Gruia ^a   Chekuri, Chandra ^b   Pál, Martin ^c   Vondrák, Jan ^d  

^a Illinois Institute of Technology   (United States)

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

^c GOOGLE INC   (United States)

^d PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATROID CONSTRAINTS; SUBMODULAR SET FUNCTION;

ALGORITHMS; CONSTRAINT THEORY; FUNCTION EVALUATION; PROBLEM SOLVING;

SET THEORY;

EID: 38049090315     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (19)

1. A. Ageev and M. Sviridenko. Pipage rounding: a new method of constructing algorithms with proven performance guarantee. J. of Combinatorial Optimization, 8:307-328, 2004.
2. C. Chekuri and A. Kumar. Maximum coverage problem with group budget constraints and applications. Proc. of APPROX, Springer LNCS, 72-83, 2004.
3. C. Chekuri and M. Pál. A recursive greedy algorithm for walks in directed graphs. Proc. of IEEE FOCS, 2005.
4. C. Chekuri and S. Khanna. A PTAS for the multiple knapsack problem. SIAM J. on Computing, 35(3):713-728, 2004.
5. G. Cornuejols, M. 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.
6. U. Feige. A threshold of Inn for approximating set cover. JACM, 45(4):634-652, 1998
7. U. Feige. On maximizing welfare when utility functions are subadditive. Proc. of ACM STOC, 41-50, 2006.
8. U. Feige and J. Vondrák. Approximation algorithms for allocation problems: Improving the Factor of 1 - 1/e. Proc. of IEEE FOCS, 667-676, 2006.
9. 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.
10. L. Fleischer, M.X. Goemans, V.S. Mirrokni and M. Sviridenko. Tight approximation algorithms for maximum general assignment problems. Proc. of ACM-SIAM SODA, 611-620, 2006.
11. E. Hazan, S. Safra and O. Schwartz. On the complexity of approximating k-set packing. Proc. of APPROX, 2003.
12. T. A. Jenkyns. The efficiency of the "greedy" algorithm. Proc. of 7th South Eastern Conference on Combinatorics, Graph Theory and Computing, 341-350, 1976.
13. B. Korte and D. Hausmann. An analysis of the greedy heuristic for independence systems. Annals of Discrete Math., 2:65-74, 1978.
14. 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.
15. R. Gandhi, S. Khuller, S. Parthasarathy and A. Srinivasan. Dependent rounding and its applications to approximation algorithms. JACM, 53(3):324-360, 2006.
16. A. Schrijver. Combinatorial optimization - polyhedra and efficiency. Springer, 2003.
17. A. Srinivasan. Distributions on level-sets with applications to approximation algorithms. Proc. of IEEE FOCS, 588-597, 2001.
18. L. Wolsey. An analysis of the greedy algorithm for the submodular set covering problem. Combinatorica, 2:385-393, 1982.
19. L. Wolsey. Maximizing real-valued submodular functions: Primal and dual heuristics for location Problems. Math, of Operations Research, 7:410-425, 1982.