Covering problems with hard capacities

SIAM Journal on Computing

Volumn 36, Issue 2, 2006, Pages 498-515

  Chuzhoy, Julia ^a,b   Naor, Joseph ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Hard capacities; Set cover; Submodular set cover; Vertex cover

Indexed keywords

HARD CAPACITIES; SET COVER; SUBMODULAR SET COVER; VERTEX COVER;

APPROXIMATION ALGORITHMS; CONSTRAINT THEORY; GRAPH THEORY; RESOURCE ALLOCATION; SET THEORY; THEOREM PROVING;

PROBLEM SOLVING;

EID: 34247184731     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539703422479     Document Type: Article

References (31)

1. E. BALAS AND M. W. PADBERG, Set partitioning: A survey, SIAM Rev., 18 (1976), pp. 710-760.
2. J. BAR-ILAN, G. KORTSARZ, AND D. PELEG, Generalized submodular cover problems and applications, in Proceedings of the 4th Israel Symposium on Theory of Computing and Systems. Jerusalem, Israel, 1996, IEEE Computer Society Press, Piscataway, NJ, 1996, pp. 110-118.
3. H. BAR-YEHUDA AND S. EVEN, A local-ratio theorem for approximating the weighted vertex cover problem, Ann. Discrete Math., 25 (1985), pp. 27-45.
4. Y. BARTAL, M. CHARIKAR, AND D. RAZ, Approximating min-sum k-clustering in metric spaces, in Proceedings of 33rd ACM Symposium on Theory of Computing, Heraklion, Crete, Greece, 2001, ACM, New York, 2001, pp. 11-20.
5. R. D. CARR, L. K. FLEISCHER, V. J. LEUNG, AND C. A. PHILLIPS, Strengthening integrality gaps for capacitated network design and covering problems, in Proceedings of the 11th ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, 2000, SIAM, Philadelphia, 2000, pp. 106-115.
6. M. CHARIKAR, S. GUHA, E. TARDOS, AND D. SHMOYS, A constant-factor approximation algorithm for the k-median problem, in Proceedings of the 31st Annual ACM Symposium on the Theory of Computing, Atlanta, GA, 1999, ACM, New York, 1999, pp. 1-10.
7. N. CHRISTOFIDES AND S. KORMAN, A computational survey of methods for the set covering problem, Management Sci., 21 (1975), pp. 591-599.
8. J. CHUZHOY AND Y. RABANI, Approximating k-median with non-uniform capacities, in Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, Canada, 2005, SIAM, Philadelphia, 2005, pp. 952-958.
9. V. CHVÁTAL, A greedy heuristic for the set-covering problem, Math. Oper. Res., 4 (1979), pp. 233-235.
10. G. DOBSON, Worst-case analysis of greedy heuristics for integer programming with non-negative data, Math. Oper. Res., 7 (1972), pp. 515-531.
11. U. FEIGE, A threshold of In n for approximating set cover, J. ACM, 45 (1998), pp. 634-652.
12. R. GANDHI, E. HALPERIN, S. KHULLER, G. KORTSARZ, AND A. SRINIVASAN, An improved approximation algorithm for vertex cover with hard capacities, in Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP), Eindhoven, The Netherlands, 2003, Lecture Notes in Comput. Sci. 2719, Springer, New York, 2003, pp. 164-175.
13. R. GANDHI, S. KHULLER, S. PARTHASARATHY, AND A. SRINIVASAN, Dependent rounding in bipartite graphs, in Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, Vancouver, BC, Canada, 2002, IEEE Press, Piscataway, NJ, pp. 323-332.
14. M. R. GAREY AND D. S. JOHNSON, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, San Francisco, 1979.
15. R. S. GARFINKEL AND G. L. NEMHAUSER, Optimal set covering: A survey, in Perspectives on Optimization: A Collection of Expository Articles, A. M. Geofrion, ed, Addison-Wesley, Reading, MA, 1972, pp. 164-193.
16. N. GARG, R. KHANDEKAR, AND V. PANDIT, Improved approximation for universal facility location, in Proceedings of the 16th ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, Canada, 2005, SIAM, Philadelphia, 2005, pp. 959-960.
17. S. GUHA, R. HASSIN, S. KHULLER, AND E. OR, Capacitated vertex covering with applications, in Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, 2002, SIAM, Philadelphia, 2002, pp. 858-865.
18. D.S. HOCHBAUM, Approximation algorithms for the set covering and vertex cover problems, SIAM J. Comput., 11 (1982), pp. 555-556.
19. D. S. HOCHBAUM, ED., Approximation Algorithms for NP-Hard Problems, PWS Publishing, Toronto, 1996.
20. D. S. JOHNSON, Approximation algorithms for combinatorial problems, J. Comput. System Sci., 9 (1974), pp. 256-278.
21. S. G. KOLLIOPOULOS AND N. E. YOUNG, Tight approximation results for general covering integer programs, in Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, Las Vegas, NV, 2001, IEEE Press, Piscataway, NJ, pp. 522-528.
22. L. LOVÁSZ, On the ratio of optimal and fractional covers, Discrete Math., 13 (1975), pp. 383-390.
23. C. LUND AND M. YANNAKAKIS, On the hardness of approximating minimization problems, J. ACM, 41 (1994), pp. 960-981.
24. M. MAHDIAN AND M. PÁL, Universal facility location, in Proceedings of the 11th Annual European Symposium on Algorithms, Budapest, Hungary, 2003, Lecture Notes in Comput. Sci. 2832, Springer, New York, 2003, pp. 409-422.
25. P. B. MIRCHANDANI AND R. L. FRANCIS, EDS., Discrete Location Theory, Wiley-Interscience, New York, 1990.
26. M. W. PADBERG, Covering, packing and knapsack problems, Ann. Discrete Math., 4 (1979), pp. 265-287.
27. D. B. SHMOYS, E. TARDOS, AND K. AARDAL, Approximation algorithms for the facility location problem, in Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, El Paso, TX, 1997, ACM, New York, 1997, pp. 265-274.
28. M. PÁL, É. TARDOS, AND T. WEXLER, Facility location with nonuniform hard capacities, in Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, Las Vegas, NV, 2001, IEEE Press, Piscataway, NJ, pp. 329-338.
29. V. V. VAZIRANI, Approximation Algorithms, Springer-Verlag, New York, 2001.
30. L. A. WOLSEY, An analysis of the greedy algorithm for the submodular set covering problem, Combinatorica, 2 (1982), pp. 385-393.
31. J. ZHANG, B. CHEN, AND Y. YE, A multi-exchange local search algorithm for the capacitated facility location problem, Math. Oper. Res., 30 (2005), pp. 389-403.