A greedy approximation algorithm for the group Steiner problem

Discrete Applied Mathematics

Volumn 154, Issue 1, 2006, Pages 15-34

  Chekuri, Chandra ^a   Even, Guy ^b   Kortsarz, Guy ^c  

^a LUCENT TECHNOLOGIES   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c RUTGERS UNIVERSITY   (United States)

Author keywords

Approximation algorithm; Combinatorial; Greedy; Group Steiner problem; Tree

Indexed keywords

APPROXIMATION THEORY; COMBINATORIAL MATHEMATICS; COMPUTER TERMINALS; GRAPH THEORY; POLYNOMIALS; PROBLEM SOLVING; TREES (MATHEMATICS);

APPROXIMATION ALGORITHMS; COMBINATORIAL; GREEDY; GROUP STEINER PROBLEMS;

ALGORITHMS;

EID: 27744491021     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2005.07.010     Document Type: Article

References (24)

1. Y. Bartal, Probabilistic approximation of metric spaces and its algorithmic applications, Proceedings of FOCS, 1996, pp. 93-184.
2. Y. Bartal, On approximating arbitrary metrics by tree metrics, Proceedings of STOC, 1998, pp. 161-168.
3. Y. Bartal, M. Charikar, D. Raz, Approximating min-sum k-clustering in metric spaces, Proceedings of STOC, 2001, pp. 11-20.
4. C.D. Bateman, C.S. Helvig, G. Robins, A. Zelikovsky, Provably good routing tree construction with multi-port terminals, Proceedings of ACM/SIGDA International Symposium on Physical Design, 1997, pp. 96-102.
5. M.M. Bern, and P. Plassmann The Steiner problem with edge lengths 1 and 2 Inform. Process. Lett. 32 1989 171 176
6. M. Charikar, C. Chekuri, T. Cheung, Z. Dai, A. Goel, S. Guha, and M. Li Approximation algorithms for directed Steiner problems J. Algorithms 33 1999 73 91
7. M. Charikar, C. Chekuri, A. Goel, S. Guha, Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median, Proceedings of STOC, 1998, pp. 114-123.
8. M. Charikar, C. Chekuri, A. Goel, S. Guha, S. Plotkin, Approximating a finite metric by small number of trees, Proceedings of FOCS, 1998, pp. 379-388.
9. G. Even, G. Kortsarz, An approximation algorithm for the Group Steiner Problem, Proceedings of SODA, 2002, pp. 49-58.
10. G. Even, G. Kortsarz, W. Slany, On network design Problems: fixed cost flows and the covering steiner Problem, Proceedings of SWAT, 2002, pp. 318-327.
11. J. Fakcharoenphol, S. Rao, K. Talwar, A tight bound on approximating arbitrary metrics by tree metrics, Proceedings of STOC, 2003, pp. 448-455.
12. U. Feige A threshold of ln n for approximating set cover J. ACM 45 1998 634 652
13. M.R. Garey, and D.S. Johnson Computers and Intractability: A Guide to the Theory of NP-Completeness 1979 W.H. Freeman and Company
14. N. Garg, G. Konjevod, and R. Ravi A polylogarithmic approximation algorithm for the Group Steiner tree problem J. Algorithms 37 2000 66 84 preliminary version in Proceedings of SODA, 1998 pp. 253-259
15. E. Halperin, G. Kortsarz, R. Krauthgamer, A. Srinivasan, N. Wang, Integrality ratio for group Steiner trees and directed Steiner trees, Proceedings of SODA, 2003, pp. 275-284.
16. E. Halperin, R. Krauthgamer, Polylogarithmic in approximability, Proceedings of STOC, 2003, pp. 585-594.
17. C.H. Helvig, G. Robins, and A. Zelikovsky Improved approximation scheme for the group Steiner problem Networks 37 1 2001 8 20
18. G. Konjevod, R. Ravi, An approximation algorithm for the covering Steiner problem, Proceedings of SODA, 2000, pp. 338-334.
19. G. Konjevod, R. Ravi, and A. Srinivasan Approximation algorithms for the covering Steiner problem Random Structures and Algorithms 20 2002 465 482
20. G. Kortsarz, and D. Peleg Approximating the weight of shallow Steiner trees Discrete Appl. Math. 93 1999 265 285
21. R. Raz, S. Safra, A sub-constant error-probability low-degree test and a sub-constant error-probability PCP characterization of NP, Proceedings of STOC, 1997, pp. 475-484.
22. G. Reich, P. Widmayer, Beyond Steiner's problem: a VLSI oriented generalization, Proceedings of Graph-Theoretic Concepts in Computer Science (WG-89), Lecture Notes in Computer Science, vol. 411, 1990, pp. 196-210.
23. A. Zelikovsky A series of approximation algorithms for the acyclic directed Steiner tree problem Algorithmica 18 1997 99 110
24. L. Zosin, S. Khuller, On directed Steiner trees, Proceedings of SODA, 2002, pp. 59-63.