Monotone submodular maximization over a matroid via non-oblivious local search

SIAM Journal on Computing

Volumn 43, Issue 2, 2014, Pages 514-542

  Filmus, Yuval ^a   Ward, Justin ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Approximation algorithms; Local search; Matroids; Submodular functions

Indexed keywords

COMBINATORIAL MATHEMATICS; MATRIX ALGEBRA; OPTIMIZATION;

APPROXIMATION RATIOS; GREEDY ALGORITHMS; LOCAL SEARCH; MAXIMUM COVERAGE; OBJECTIVE FUNCTIONS; POTENTIAL FUNCTION; SUBMODULAR FUNCTIONS; SUBMODULAR OPTIMIZATIONS;

APPROXIMATION ALGORITHMS;

EID: 84899637019     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/130920277     Document Type: Conference Paper

References (37)

1. A. A. Ageev and M. I. Sviridenko, Pipage rounding: A new method of constructing algorithms with proven performance guarantee, J. Comb. Optim., 8 (2004), pp. 307-328.
2. P. Alimonti, New local search approximation techniques for maximum generalized satisfiability problems, in CIAC: Proceedings of the 2nd Italian Conference on Algorithms and Complexity, Springer-Verlag, New York, 1994, pp. 40-53.
3. B. V. Ashwinkumar and J. Vondr'ak, Fast algorithms for maximizing submodular functions, in Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, 2014, pp. 1497-1514.
4. R. A. Brualdi, Comments on bases in dependence structures, Bull. Austral. Math. Soc., 1 (1969), pp. 161-167.
5. N. Buchbinder, M. Feldman, J. (Seffi) Naor, and R. Schwartz, A tight linear time (1/2)-approximation for unconstrained submodular maximization, in FOCS, IEEE, Piscataway, NJ, 2012, pp. 649-658.
6. N. Buchbinder, M. Feldman, J. (Seffi) Naor, and R. Schwartz, Submodular maximization with cardinality constraints, in Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, 2014, pp. 1433-1452.
7. G. Calinescu, C. Chekuri, M. P'al, and J. Vondr'ak, Maximizing a submodular set function subject to a matroid constraint (Extended abstract), in 12th International IPCO Conference on Integer Programming and Combinatorial Optimization, Springer, Berlin, 2007, pp. 182-196.
8. G. Calinescu, C. Chekuri, M. Ṕal, and J. Vondŕak, Maximizing a monotone submodular function subject to a matroid constraint, SIAM J. Comput., 40 (2011), pp. 1740-1766.
9. C. Checkuri, J. Vondr'ak, and R. Zenklusen, Submodular function maximization via the multilinear relaxation and contention resolution schemes, STOC, San Jose, CA, 2011.
10. C. Chekuri, J. Vondrak, and R. Zenklusen, Dependent randomized rounding via exchange properties of combinatorial structures, in Proceedings of the 2010 IEEE 51st Annual Symposium on FOCS, IEEE, Piscataway, NJ, 2010, pp. 575-584.
11. J. Edmonds, Matroids and the greedy algorithm, Math. Program., 1 (1971), pp. 127-136.
12. U. Feige, A threshold of ln n for approximating set cover, J. ACM, 45 (1998), pp. 634-652.
13. U. Feige, V. S. Mirrokni, and J. Vondrak, Maximizing non-monotone submodular functions, in FOCS, IEEE, Piscataway, NJ, 2007, pp. 461-471.
14. M. Feldman, J. Naor, and R. Schwartz, A unified continuous greedy algorithm for submodular maximization, in FOCS, IEEE, Piscataway, NJ, 2011, pp. 570-579.
15. M. Feldman, J. (Seffi) Naor, and R. Schwartz, Nonmonotone submodular maximization via a structural continuous greedy algorithm, in ICALP, Springer-Verlag, New York, 2011, pp. 342-353.
16. M. Feldman, J. (Seffi) Naor, R. Schwartz, and J. Ward, Improved approximations for k-exchange systems, in 19th Annual European Symposium on Algorithms, Saarbrucken, Germany, Springer, New York, 2011, pp. 784-798.
17. Y. Filmus and J. Ward, The power of local search: Maximum coverage over a matroid, in STACS, Leibniz-Zentrum fur Informatik GmbH, Schloss Dagstuhl, Wadern, Germany, 2012, pp. 601-612.
18. Y. Filmus and J. Ward, A tight combinatorial algorithm for submodular maximization subject to a matroid constraint, in FOCS, IEEE, Piscataway, NJ, 2012, pp. 659-668.
19. Y. Filmus and J. Ward, A Tight Combinatorial Algorithm for Submodular Maximization Subject to a Matroid Constraint, preprint, arXiv:1204.4526, 2012.
20. M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey, An analysis of approximations for maximizing submodular set functions-II, in Polyhedral Combinatorics, Springer, Berlin, 1978, pp. 73-87.
21. M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Res. Logist., 3 (1956), pp. 95-110.
22. S. Oveis Gharan and J. Vondr'ak, Submodular maximization by simulated annealing, in SODA, SIAM, Philadelphia, 2011, pp. 1098-1116.
23. M. X. Goemans and J. Kleinberg, An improved approximation ratio for the minimum latency problem, Math. Program., 82 (1998), pp. 111-124.
24. P. R. Goundan and A. S. Schulz, Revisiting the Greedy Approach to Submodular Set Function Maximization, manuscript, 2007.
25. K. Jain, M. Mahdian, E. Markakis, A. Saberi, and V. V. Vazirani, Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP, J. ACM, 50 (2003), pp. 795-824.
26. S. Khanna, R. Motwani, M. Sudan, and U. Vazirani, On syntactic versus computational views of approximability, SIAM J. Comput., 28 (1999), pp. 164-191.
27. S. Khuller, A. Moss, and J. (Seffi) Naor, The budgeted maximum coverage problem, Inform. Process. Lett., 70 (1999), pp. 39-45.
28. J. Lee, V. S. Mirrokni, V. Nagarajan, and M. Sviridenko, Non-monotone submodular maximization under matroid and knapsack constraints, in STOC, ACM, New York, 2009, pp. 323-332.
29. J. Lee, M. Sviridenko, and J. Vondŕak, Submodular maximization over multiple matroids via generalized exchange properties, Math. Oper. Res., 35 (2010), pp. 795-806.
30. G. L. Nemhauser and L. A. Wolsey, Best algorithms for approximating the maximum of a submodular set function, Math. Oper. Res., 3 (1978), pp. 177-188.
31. G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher, An analysis of approximations for maximizing submodular set functions-I, Math. Program., 14 (1978), pp. 265-294.
32. R. Rado, Note on independence functions, Proc. London Math. Soc. (3), 7 (1957), pp. 300-320.
33. M. Sviridenko and J. Ward, Tight Bounds for Submodular and Supermodular Optimization with Bounded Curvature, preprint, arXiv:1311.4728, 2013.
34. J. Vondr'ak, Optimal approximation for the submodular welfare problem in the value oracle model, in STOC, ACM, New York, 2008, pp. 67-74.
35. J. Vondr'ak, Submodularity and curvature: The optimal algorithm, in RIMS Kokyuroku Bessatsu B23, S. Iwata, ed., Kyoto University, Kyoto, 2010, pp. 253-266.
36. J. Ward, A (k + 3)/2-approximation algorithm for monotone submodular k-set packing and general k-exchange systems, in STACS, Leibniz-Zentrum fur Informatik GmbH, Schloss Dagstuhl, Wadern, Germany, 2012, pp. 42-53.
37. J. Ward, Oblivious and Non-Oblivious Local Search for Combinatorial Optimization, Ph.D. thesis, University of Toronto, Toronto, 2012.