Polynomial-time approximation schemes for subset-connectivity problems in bounded-genus graphs

Leibniz International Proceedings in Informatics, LIPIcs

Volumn 3, Issue , 2009, Pages 171-182

  Borradaile, Glencora ^a   Demaine, Erik D ^b   Tazari, Siamak ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Bounded genus graph; Embedded graph; Polynomial time approximation scheme; Steiner tree; Subset TSP; Survivable network design

Indexed keywords

BOUNDED-GENUS GRAPHS; EMBEDDED GRAPHS; POLYNOMIAL TIME APPROXIMATION SCHEMES; STEINER TREES; SUBSET TSP;

COMPUTER SCIENCE; FORESTRY; GRAPHIC METHODS; PROGRAM PROCESSORS; SET THEORY;

GRAPH THEORY;

EID: 84880200521     PISSN: 18688969     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. S. Arnborg and A. Proskurowski. Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Applied Mathematics, 23(1):11-24, 1989.
2. S. Arora. Approximation schemes for NP-hard geometric optimization problems: A survey. Mathematical Programming, 97(1-2):43-69, 2003.
3. G. Borradaile and P. N. Klein. The two-edge connectivity survivable network problem in planar graphs. In ICALP '08: Proceedings of the 35th International Colloquium on Automata, Languages and Programming, volume 5125 of Lecture Notes in Computer Science, pages 485-501. Springer, 2008.
4. G. Borradaile, C. Mathieu, and P. N. Klein. A polynomial-time approximation scheme for Steiner tree in planar graphs. In SODA '07: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1285-1294, 2007.
5. G. Borradaile, P. N. Klein, and D. Pritchard. A polynomial-time approximation scheme for the survivable network problem in planar graphs. In preparation.
6. G. Borradaile, C. Mathieu, and P. N. Klein. Steiner tree in planar graphs: An O(n log n) approximation scheme with singly exponential dependence on epsilon. In WADS '07: Proceedings of the 10th Workshop on Algorithms and Data Structures, volume 4619 of Lecture Notes in Computer Science, pages 275-286. Springer, 2007.
7. S. Cabello and E. W. Chambers. Multiple source shortest paths in a genus g graph. In SODA '07: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 89-97, Philadelphia, PA, USA, 2007.
8. E. D. Demaine, M. Hajiaghayi, and B. Mohar. Approximation algorithms via contraction decomposition. In SODA '07: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 278-287, Philadelphia, PA, USA, 2007.
9. R. E. Erickson, C. L. Monma, and Jr. A. F. Veinott. Send-and-split method for minimum-concave-cost network flows. Math. Oper. Res., 12(4):634-664, 1987.
10. D. Eppstein. Dynamic generators of topologically embedded graphs. In SODA '03: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 599-608, Philadelphia, PA, USA, 2003.
11. J. Erickson and K. Whittlesey. Greedy optimal homotopy and homology generators. In SODA '05: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1038-1046, Philadelphia, PA, USA, 2005.
12. M. Henzinger, P. N. Klein, S. Rao, and S. Subramanian. Faster shortest-path algorithms for planar graphs. Journal of Computer and System Sciences, 55(1):3-23, 1997.
13. P. N. Klein. A subset spanner for planar graphs, with application to subset TSP. In STOC '06: Proceedings of the 38th ACM Symposium on Theory of Computing, pages 749-756, 2006.
14. E. Korach and N. Solel. Linear time algorithm for minimum weight Steiner tree in graphs with bounded treewidth. Manuscript, 1990.
15. K. Mehlhorn. A faster approximation algorithm for the Steiner problem in graphs. Information Processing Letters, 27:125-128, 1988.
16. B. Mohar. A linear time algorithm for embedding graphs in an arbitrary surface. SIAM Journal on Discrete Mathematics, 12(1):6-26, 1999.
17. B. Mohar and C. Thomassen. Graphs on Surfaces. The John Hopkins University Press, 2001.
18. N. Robertson and P. D. Seymour. Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms, 7(3):309-322, 1986.
19. S. Tazari and M. Müller-Hannemann. Shortest paths in linear time on minor-closed graph classes, with an application to Steiner tree approximation. Discrete Applied Mathematics, in press, 2008.
20. An extended abstract appeared in WG '08: Proceedings of the 34th Workshop on Graph Theoretic Concepts in Computer Science, LNCS 5344, pp. 360-371, Springer, 2008.