A unified approach to approximating partial covering problems

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

Volumn 4168 LNCS, Issue , 2006, Pages 468-479

  Könemann, Jochen ^a   Parekh, Ojas ^b   Segev, Danny ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b EMORY UNIVERSITY   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COST EFFECTIVENESS; OPTIMIZATION; SET THEORY;

APPROXIMABILITY; PARTIAL COVER PROBLEMS; PROBLEM SPECIFIC CONNECTIONS;

PROBLEM SOLVING;

EID: 33750684328     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11841036_43     Document Type: Conference Paper

References (32)

1. N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, and J. Naor. A general approach to online network optimization problems. In Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 577-586, 2004.
2. E. Balas and M. Padberg. Set partitioning: A survey. SIAM Review, 18(4):710-760, 1976.
3. R. Bar-Yehuda. Using homogeneous weights for approximating the partial cover problem. Journal of Algorithms, 39(2): 137-144, 2001.
4. N. H. Bshouty and L. Burroughs. Massaging a linear programming solution to give a 2-approximation for a generalization of the vertex cover problem. In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, pages 298-308, 1998.
5. S. Chawla, R. Krauthgamer, R. Kumar, Y. Rabani, and D. Sivakumar. On the hardness of approximating multicut and sparsest-cut. In Proceedings of the 20th Annual IEEE Conference on Computational Complexity, pages 144-153, 2005.
6. F. A. Chudak, T. Roughgarden, and D. P. Williamson. Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation. Mathematical Programming, 100(2):411-421, 2004.
7. W. J. Cook, W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver. Combinatorial Optimization. John Wiley and Sons, New York, 1997.
8. J. Edmonds and E. L. Johnson. Matching: A well-solved class of integer linear programs. In Combinatorial Structures and their Applications, pages 89-92. Gordon and Breach, New York, 1970.
9. G. Even, J. Feldman, G. Kortsarz, and Z. Nutov. A 3/2-approximation algorithm for augmenting the edge-connectivity of a graph from 1 to 2 using a subset of a given edge set. In Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, pages 90-101, 2001.
10. U. Feige. A threshold of In n for approximating set cover. Journal of the ACM, 45(4):634-652, 1998.
11. T. Fujito. On approximation of the submodular set cover problem. Operations Research Letters, 25(4): 169-174, 1999.
12. R. Gandhi, S. Khuller, and A. Srinivasan. Approximation algorithms for partial covering problems. Journal of Algorithms, 53(1):55-84, 2004.
13. R. S. Garfinkel and G. L. Nemhauser. Optimal set covering: A survey. In A. M. Geoffrion, editor, Perspectives on Optimization, pages 164-183, 1972.
14. N. Garg, V. V. Vazirani, and M. Yannakakis. Approximate max-flow min-(multi)cut theorems and their applications. SIAM Journal on Computing, 25(2):235-251, 1996.
15. N. Garg, V. V. Vazirani, and M. Yannakakis. Primal-dual approximation algorithms for integral flow and multicut in trees. Algorithmica, 18(1):3-20, 1997.
16. D. R. Gaur, T. Ibaraki, and R. Krishnamurti. Constant ratio approximation algorithms for the rectangle stabbing problem and the rectilinear partitioning problem. Journal of Algorithms, 43(1):138-152, 2002.
17. D. Golovin, V. Nagarajan, and M. Singh. Approximating the k-multicut problem. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 621-630, 2006.
18. D. S. Hochbaum. Approximating covering and packing problems: Set cover, vertex cover, independent set, and related problems. In D. S. Hochbaum, editor, Approximation Algorithms for NP-Hard Problems, chapter 3, pages 94-143. PWS Publishing Company, 1997.
19. D. S. Hochbaum. The t-vertex cover problem: Extending the half integrality framework with budget constraints. In Proceedings of the 1st International Workshop on Approximation Algorithms for Combinatorial Optimization, pages 111-122, 1998.
20. D. S. Johnson. Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences, 9(3):256-278, 1974.
21. M. J. Kearns. The Computational Complexity of Machine Learning. MIT Press, 1990.
22. S. Khot. On the power of unique 2-prover 1-round games. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pages 767-775, 2002.
23. J. Könemann, O. Parekh, and D. Segev. A unified approach to approximating partial covering problems, 2006. Available at http://www.math.tau. ac.il/~segevd.
24. A. Levin and D. Segev. Partial multicuts in trees. In Proceedings of the 3rd International Workshop on Approximation and Online Algorithms, pages 320-333, 2005.
25. L. Lovász. On the ratio of optimal integral and fractional covers. Discrete Mathematics, 13:383-390, 1975.
26. K. G. Murty and C. Perin. A 1-matching blossom type algorithm for edge covering problems. Networks, 12:379-391, 1982.
27. H. Nagamochi. An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning tree. Discrete Applied Mathematics, 126(1):83-113, 2003.
28. M. W. Padberg. Covering, packing and knapsack problems. Annals of Discrete Mathematics, 4:265-287, 1979.
29. O. Parekh. Polyhedral Techniques for Graphic Covering Problems. PhD thesis, Department of Mathematical Sciences, Carnegie Mellon University, 2002.
30. J. Plesník. Constrained weighted matchings and edge coverings in graphs. Discrete Applied Mathematics, 92(2-3):229-241, 1999.
31. H. Räcke. Minimizing congestion in general networks. In Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, pages 43-52, 2002.
32. P. Slavík. Improved performance of the greedy algorithm for partial cover. Information Processing Letters, 64(5):251-254, 1997.