A polynomial-time approximation scheme for Steiner tree in planar graphs

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 1285-1294

  Borradaile, Glencora ^a   Kenyon Mathieu, Claire ^a   Klein, Philip ^a  

^a Brown Univerity   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; GRAPH THEORY; GRAPHIC METHODS; POLYNOMIAL APPROXIMATION;

APPROXIMATION SCHEME; PLANAR GRAPH; POLYNOMIAL TIME APPROXIMATION SCHEMES; STEINER TREES;

TREES (MATHEMATICS);

EID: 84969151285     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. S. Arora. Polynomial-time approximation schemes for euclidean TSP and other geometric problems. JACM, 45(5):753-782, 1998.
2. S. Arora, M. Grigni, D. Karger, P. Klein, and A. Woloszyn. A polynomial-time approximation scheme for weighted planar graph TSP. In 9th SODA, pages 33-41, 1998.
3. B. Baker. Approximation algorithms for NP-complete problems on planar graphs. JACM, 41(1):153-180, 1994.
4. M. Bern. Faster exact algorithms for steiner trees in planar networks. Networks, 20:109-120, 1990.
5. M. Bern and D. Bienstock. Polynomially solvable special cases of the steiner problem in planar networks. Annals of Operations Research, 33:405-418, 1991.
6. M. Bern and P. Plassmann. The Steiner problem with edge lengths 1 and 2. IPL, 32:171-176, 1989.
7. R. E. Erickson, C. L. Monma, and A. F. Veinott. Sendand-split method for minimum concave-cost network flows. Mathematics of Operations Research, 12:634-664, 1987.
8. I. Hicks, A. Koster, and E. Kolotoǧlu. Branch and tree decomposition techniques for discrete optimization. In J. Smith, editor, TutORials 2005, INFORMS TutO-Rials in Operations Research Series, chapter 1, pages 1-29. INFORMS Annual Meeting, 2005.
9. P. Klein. A linear-time approximation scheme for planar weighted TSP. In 46th FOCS, pages 647-647, 2005.
10. P. Klein. A subset spanner for planar graphs, with application to subset TSP. In 38th STOC, pages 749-756, 2006.
11. L. Kou, G. Markowsky, and L. Berman. A fast algorithm for Steiner trees. Acta Informatica, 15:141-145, 1981.
12. K. Mehlhorn. Approximation algorithm for the Steiner problem in graphs. IPL, 27(3):125-128, 1988.
13. J. S. Provan. An approximation scheme for finding steiner trees with obstacles. SIAM Journal on Computing, 17:920-934, 1988.
14. J. S. Provan. Convexity and the steiner tree problem. Networks, 1988.
15. S. Rao and W. Smith. Approximating geometrical graphs via "spanners" and "banyans". In ACM Symposium on Theory of Computing, pages 540-550, 1998.
16. H. Takahashi and A. Matsuyama. An approximate solution for the steiner problem in graphs. Mathematica Japonicae, 24:571-577, 1980.
17. P. Widmayer. A fast approximation algorithm for Steiner's problem in graphs. In Graph-Theoretic Concepts in Computer Science, volume 246 of LNCS, pages 17-28. Springer Verlag, 1986.
18. Y. Wu, P. Widmayer, and C. Wong. A faster approx-imation algorithm for the Steiner problem in graphs. Acta informatica, 23(2):223-229, 1986.