Metric Embeddings - Beyond One-Dimensional Distortion

Discrete and Computational Geometry

Volumn 31, Issue 3, 2004, Pages 339-356

  Krauthgamer, Robert ^a   Linial, Nathan ^b   Magen, Avner ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842765524     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-003-2872-2     Document Type: Article

References (16)

1. [BCD] A. Brandstädt, V. Chepoi, and F. Dragan. Distance approximating trees for chordal and dually chordal graphs. J. Algorithms, 30(1):166-184, 1999.
2. [B1] J. Bourgain. On Lipschitz embedding of finite metric spaces in Hilbert space. Israel J. Math., 52(1-2):46-52, 1985.
3. [B2] J. Bourgain. The metrical interpretation of superreflexivity in Banach spaces. Israel J. Math., 56(2):222-230, 1986.
4. [DV] J. Dunagan and S. Vempala. On Euclidean embeddings and bandwidth minimization. In Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (Editors: MX. Goemans, K. Jansen, J. Rolim, and L. Trevisan), pages 229-240. Volume 2129 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, 2001.
5. p-spaces. Ark. Mat., 8:103-105, 1969.
6. [F] U. Feige. Approximating the bandwidth via volume respecting embeddings. J. Comput. System Sci., 60(3):510-539, 2000.
7. [G] A. Gupta. Embeddings of Finite Metrics. Ph.D. thesis, University of California, Berkeley, CA, August 2000.
8. [I] P. Indyk. Algorithmic applications of low-distortion geometric embeddings. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pages 10-33, October 2001.
9. [L] N. Linial. Finite metric spaces - combinatorics, geometry and algorithms. In Proceedings of the International Congress of Mathematicians, volume III, pages 573-586, 2002.
10. [LLR] N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15(2):215-245, 1995.
11. [LM] N. Linial and A. Magen. Least-distortion Euclidean embeddings of graphs: products of cycles and expanders. J. Combin. Theory Ser. B, 79(2):157-171, 2000.
12. [LS] N. Linial and M. Saks. The Euclidean distortion of complete binary trees. Discrete Comput. Geom., 29(1):19-21, 2003.
13. p spaces. Israel J. Math., 102:189-197, 1997.
14. [M2] J. Matoušek. On embedding trees into uniformly convex Banach spaces. Israel J. Math., 114:221-237, 1999.
15. [M3] J. Matoušek. Lectures on Discrete Geometry. Volume 212 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2002.
16. [R] S. Rao. Small distortion and volume preserving embeddings for planar and Euclidean metrics. In Proceedings of the 15th Annual Symposium on Computational Geometry, pages 300-306. ACM, New York, 1999.