Cuts, trees and l1-embeddings of graphs

Combinatorica

Volumn 24, Issue 2, 2004, Pages 233-269

  Gupta, Anupam ^a   Newman, Ilan ^b   Rabinovich, Yuri ^b   Sinclair, Alistair ^c  

^a Carnegie Mellon University   (United States)

^b UNIVERSITY OF HAIFA   (Israel)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042792353     PISSN: 02099683     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00493-004-0015-x     Document Type: Article

References (43)

1. NOGA ALON, RICHARD M. KARP, DAVID PELEG and DOUGLAS B. WEST: A graphtheoretic game and its applications to the k-server problem, SIAM Journal on Computing 24(1) (1995), 78-100.
2. YONATAN AUMANN and YUVAL RABANI: An O(log k) approximate min-cut max-flow theorem and approximation algorithm, SIAM Journal on Computing 27(1) (1998), 291-301.
3. BARUCH AWERBUCH and YOSSI AZAR: Buy-at-bulk network design, in Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, pages 542-547, 1997.
4. YAIR BARTAL: Probabilistic approximations of metric spaces and its algorithmic applications, in Proceedings of the 31th Annual IEEE Symposium on Foundations of Computer Science, pages 184-193, 1996.
5. YAIR BARTAL: On approximating arbitrary metrics by tree metrics, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing, pages 161-168, 1998.
6. YAIR BARTAL, AVRIM BLUM, CARL BURCH and ANDREW TOMKINS: A polylog(n)-competitive algorithm for metrical task systems, in Proceedings of the 29th Annual ACM Sywposium on Theory of Computing, pages 711-719, 1997.
7. SANDEEP N. BHATT and F. THOMAS LEIGHTON: A framework for solving VLSI graph layout Problems, Journal of Computer and System Sciences 28(2) (1984), 300-343.
8. AVRIM BLUM GORAN KONJEVOD, R. RAVI and SANTOSH VEMPALA: Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems, Theoretical Computer Science 235(1) (2000), 25-42. (Preliminary version in 30th Annual ACM Symposium on Theory of Computing, pages 100-105, 1998.)
9. AVRIM BLUM GORAN KONJEVOD, R. RAVI and SANTOSH VEMPALA: Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems, Theoretical Computer Science 235(1) (2000), 25-42. (Preliminary version in 30th Annual ACM Symposium on Theory of Computing, pages 100-105, 1998.)
10. JEAN BOURGAIN: On Lipschitz embeddings of finite metric spaces in Hubert space, Israel Journal of Mathematics 52(1-2) (1985), 46-52.
11. MOSES CHARIKAR, CHANDRA CHEKURI, ASHISH GOEL and SUDIPTO GUHA: Rounding via trees: deterministic approximation algorithms for group Steiner trees and k median, in Proceedings of the 30th Annual ACM Symposium an Theory of Computing, pages 114-123, 1998.
12. MOSES CHARIKAR, CHANDRA CHEKURI, ASHISH GOEL, SUDIPTO GUHA and SERGE A. PLOTKIN: Approximating a finite metric by a small number of tree metrics, in Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, pages 379-388, 1998.
13. MOSES CHARIKAR and BALAJI RAGHAVACHARI: The finite capacity dial-a-ride problem, in Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, pages 458-467, 1998.
14. 1, in Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 527-536, 2003.
15. VICTOR CHEPOI and BERNARD FICHET: A note on circular decomposable metrics, Geometriae.Dedicata 69(3) (1998), 237-240.
16. MICHEL MARIE DEZA and MONIQUE LAURENT: Geometry of Cuts and Metrics, Springer Verlag, Berlin, 1997.
17. REINHARD DIESTEL: Graph Theory, Springer-Verlag, New York, 1997.
18. JITTAT FAKCHAROENPHOL, SATISH RAO and KUNAL TALWAR: A tight bound on approximating arbitrary metrics be tree metrics, in Proceedings of the thirty-fifth ACM symposium on Theory of computing, pages 448-455, 2003.
19. URIEL FEIGE: Approximating the bandwidth via volume respecting embeddings, Journal of Computer and System Sciences 60(3) (2000), 510-539.
20. ANDRÁS FRANK: Packing paths, circuits, and cuts - a survey. In Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, editors, Paths, Flows and VLSI-Layout, pages 47-100. Springer-Verlag, 1990.
21. Naveen Garg, Goran Konjevod and R. RAVI: A polylogarithmic approximation algorithm for the group Steiner tree problem, Journal of Algorithms 37(1) (2000), 66-84. (Preliminary version in 9th Annual ACM-SIAM Symposium on Discrete Al-gorithms, pages 253-259, 1998.)
22. Naveen Garg, Goran Konjevod and R. RAVI: A polylogarithmic approximation algorithm for the group Steiner tree problem, Journal of Algorithms 37(1) (2000), 66-84. (Preliminary version in 9th Annual ACM-SIAM Symposium on Discrete Al-gorithms, pages 253-259, 1998.)
23. MAKOTO IMASE and BERNARD M. WAXMAN: Dynamic Steiner tree problem, SIAM J. Discrete Math. 4(3) (1991), 369-384.
24. RICHARD M. KARP: A 2k-competitive algorithm for the circle. Manuscript, 1989.
25. PHILIP KLEIN, SERGE A. PLOTKIN and SATISH B. RAO: Excluded minors, network decomposition, and multicommodity flow; in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 682-690, 1993.
26. Philip Klein, Satish Rao, Ajit Agrawal and R. RAVI: An approximate max-flow min-cut relation for undirected multicommodity flow, with applications; Combinatorica 15(2) (1995), 187-202.
27. GORAN KONJEVOD, R. RAVI and F. SIBEL SALMAN: On approximating planar metrics by tree metrics, Information Processing Letters 80(4) (2001), 213-219.
28. F. THOMAS LEIGHTON and SATISH B. RAO: Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms, Journal of the ACM 46(6) (1999), 787-832. (Preliminary version in 29th Annual Symposium on Foundations of Computer Science, pages 422-431, 1988.)
29. F. THOMAS LEIGHTON and SATISH B. RAO: Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms, Journal of the ACM 46(6) (1999), 787-832. (Preliminary version in 29th Annual Symposium on Foundations of Computer Science, pages 422-431, 1988.)
30. NATHAN LINIAL, ERAN LONDON and YURI RABINOVICH: The geometry of graphs and some of its algorithmic applications, Combinatorica 15(2) (1995) 215-245. (Preliminary version in 35th Annual Symposium on Foundations of Computer Science, pages 577-591, 1994.)
31. NATHAN LINIAL, ERAN LONDON and YURI RABINOVICH: The geometry of graphs and some of its algorithmic applications, Combinatorica 15(2) (1995) 215-245. (Preliminary version in 35th Annual Symposium on Foundations of Computer Science, pages 577-591, 1994.)
32. ILAN NEWMAN and YURI RABINOVICH: A lower bound on the distortion of embedding planar metrics into Euclidean space, in 18th Annual ACM Symposium on Computational Geometry, pages 94-96, 2002.
33. ILAN NEWMAN, YURI RABINOVICH and MICHAEL SAKS: unpublished notes.
34. HARUKO OKAMURA and PAUL D. SEYMOUR: Multicommodity flows in planar graphs, Journal of Combinatorial Theory, Series B 31(1) (1981), 75-81.
35. JAMES K. PARK and CYNTHIA A. PHILLIPS: Finding minimum-quotient cuts in planar graphs (extended abstract), in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pages 766-775, 1993.
36. YURI RABINOVICH and RAN RAZ: Lower bounds on the distortion of embedding finite metric spaces in graphs, Discrete & Computational Geometry 19(1) (1998), 79-94.
37. SATISH B. RAO: Faster algorithms for finding small edge cuts in planar graphs, in Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 229-240, 1992.
38. SATISH B. RAO: Small distortion and volume preserving embeddings for planar and Euclidean metrics, in 15th Annual ACM Symposium on Computational Geometry, pages 300-306, 1999.
39. ALEXANDER SCHRIJVER: Homotopic routing methods, in Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, editors, Paths, Flows and VLSI-Layout, pages 329-371. Springer-Verlag, 1990.
40. DAVID B. SHMOYS: Cut problems and their application to divide-and-conquer, in Dorit S. Hochbaum, editor, Approximation Algorithms for NP-hard Problems, pages 192-235. PWS Publishing, 1997.
41. BANG YE Wu, GIUSEPPE LANCIA, VINEET BAFNA, KUN-MAO CHAO, R. RAVI and CHUAN YI TAN: A polynomial time approximation scheme for minimum routing cost spanning trees, SIAM Journal on Computing 20(3) (1999), 761-778. (Preliminary version in 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 21-32, 1998.)
42. BANG YE Wu, GIUSEPPE LANCIA, VINEET BAFNA, KUN-MAO CHAO, R. RAVI and CHUAN YI TAN: A polynomial time approximation scheme for minimum routing cost spanning trees, SIAM Journal on Computing 20(3) (1999), 761-778. (Preliminary version in 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 21-32, 1998.)
43. ANDREW CHI-CHIH YAO: Probabilistic computations: Toward a unified measure of complexity, in Proceedings of the 18th Annual IEEE Symposium on Foundations of Computer Science, pages 222-227, 1977.