The set connector problem in graphs

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

Volumn 4513 LNCS, Issue , 2007, Pages 484-498

  Fukunaga, Takuro ^a   Nagamochi, Hiroshi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; COST FUNCTIONS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; THEOREM PROVING;

SET CONNECTOR PROBLEMS; SET CONNECTORS; STEINER FOREST PROBLEM;

GRAPH THEORY;

EID: 38049052468     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-72792-7_36     Document Type: Conference Paper

References (28)

1. E. M. Arkin, M. M. Halldórsson, and R. Hassin, Approximating the tree and tour covers of a graph, Information Processing Letters, 47 (1993), pp. 275-282.
2. C. D. Bateman, C. S. Helvig, G. Robins, and A. Zelikovsky, Provably good routing tree construction with multi-port terminals, in Proceedings of the 1997 International Symposium on Physical Design, 1997, pp. 96-102.
3. M. Charikar, C. Chekuri, A. Goel, and S. Guha, Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median, in Proceedings of the thirtieth Annual ACM Symposium on Theory of Computing, 1998, pp. 114-123.
4. C. Chekuri, G. Even, and G. Kortsarzc, A greedy approximation algorithm for the group Steiner problem, Discrete Applied Mathematics, 154 (2006), pp. 15-34.
5. C. Chekuri and F. B. Shepherd, Approximate integer decompositions for undirected network design problems. Manuscript, 2004.
6. D. E. Drake and S. Hougardy, On approximation algorithms for the terminal Steiner tree problem, Information Processing Letters, 89 (2004), pp. 15-18.
7. A. Frank, On a theorem of Mader, Discrete Mathematics, 191 (1992), pp. 49-57.
8. T. Fujito, On approximability of the independent/connected edge dominating set problems, Information Processing Letters, 79 (2001), pp. 261-266.
9. T. Fujito, How to trim an MST: A 2-approximation algorithm for minimum cost tree cover, in Proceedings of Automata, Languages and Programming, 33rd International vol. 4051 of Lecture Notes in Computer Science, Venice, Italy, 2006, pp. 431-442.
10. N. Garg, G. Konjevod, and R. Ravi, A polylogarithmic approximation algorithm for the group Steiner tree problem, Journal of Algorithms, 37 (2000), pp. 66-84.
11. M. X. Goemans and D. P. Williamson, A general approximation technique for constrained forest problems, SIAM Journal on Computing, 24 (1995), pp. 296-317.
12. D. Gusfield, Connectivity and edge-disjoint spanning trees, Information Processing Letters, 16 (1983), pp. 87-89.
13. E. Halperin, G. Kortsarz, R. Krauthgamer, A. Srinivasan, and N. Wang, Integrality ratio for group Steiner trees and directed steiner trees, in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 2003, pp. 275-284.
14. E. Halperin and R. Krauthgamer, Polylogarithmic inapproximability, in Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, 2003, pp. 585-594.
15. T. Ishii and M. Hagiwara, Augmenting local edge-connectivity between vertices and vertex subsets in undirected graphs, in Proceedings of 28th International Symposium on Mathematical Foundations of Computer Science, vol. 2747 of Lecture Notes in Computer Science, 2003, pp. 490-499.
16. H. Ito, Node-to-area connectivity of graphs, Transactions of the Institute of Electrical Engineers of Japan, 11C (1994), pp. 463-469.
17. H. Ito and M. Yokoyama, Edge connectivity between nodes and node-subsets, Networks, 31 (1998), pp. 157-164.
18. J. Könemann, G. Konjevod, O. Parekh, and A. Sinha, Improved approximations for tour and tree covers, Algorithmica, 38 (2004), pp. 441-449.
19. G. Lin and G. Xue, On the terminal Steiner tree problem, Information Processing Letters, 84 (2002), pp. 103-107.
20. C. L. Lu, C. Y. Tang, and R. C.-T. Lee, The full Steiner tree problem, Theoretical Computer Science, 306 (2003), pp. 55-67.
21. W. Mader, A reduction method for edge-connectivity in graphs, Annals of Discrete Mathematics, 3 (1978), pp. 145-164.
22. H. Miwa and H. Ito, Edge augmenting problems for increasing connectivity between vertices and vertex subsets, in 1999 Technical Report of IPSJ, vol. 99-AL-66, 1999, pp. 17-24.
23. Z. Nutov, Approximating connectivity augmentation problems, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, 2005, pp. 176-185.
24. G. Reich and P. Widmayer, Beyond Steiner's problem: a VLSI oriented generalization, in Proceedings of Graph-Theoretic Concepts in Computer Science, vol. 411 of Lecture Notes in Computer Science, 1990, pp. 196-210.
25. A. Schrijver, Combinatorial Optimization: Polyhedra and Efficiency, Springer, 2003.
26. P. Slavík, Approximation algorithms for set cover and related problems, PhD thesis, University of New York, 1998.
27. E. Tardos, A strongly polynomial algorithm to solve combinatorial linear programs, Operations Research, 34 (1986), pp. 250-256.
28. L. Zosin and S. Khuller, On directed Steiner trees, in Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, 2002, pp. 59-63.