Approximation algorithms for low-distortion embeddings into low-dimensional spaces

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2005, Pages 119-128

  Bǎdoiu, Mihai ^a   Dhamdhere, Kedar ^b   Gupta, Anupam ^b   Rabinovich, Yuri ^c   Räcke, Harald ^b   Ravi, R ^d   Sidiropoulos, Anastasios ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Carnegie Mellon University   (United States)

^c UNIVERSITY OF HAIFA   (Israel)

^d CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; EMBEDDING DISTANCE MATRICES; GEOMETRIC STRUCTURES; MULTI-DIMENSIONAL SCALING (MDS);

CONFORMAL MAPPING; GRAPH THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; METRIC SYSTEM; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; TREES (MATHEMATICS);

ALGORITHMS;

EID: 20744450090     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. +96] R. Agarwala, V. Bafna, M. Farach-Colton, B. Narayanan, M. Paterson, and M. Thorup. On the approximability of numerical taxonomy: (fitting distances by tree metrics). 7th Symposium on Discrete Algorithms, 1996.
2. [BIR03] M. Badoiu, P. Indyk, and Y. Rabinovich. Approximate algorithms for embedding metrics into low-dimensional spaces. Manuscript, 2003.
3. +03] Z. Bar-Joseph, E. D. Demaine, D. K. Gifford, A. M. Hamel, Tommi S. Jaakkola, and Nathan Srebro. K-ary clustering with optimal leaf ordering for gene expression data. Bioinformatics, 19(9):1070-8, 2003.
4. [Bor33] K. Borsuk. Drei Sätze über die n-dimensionale euklidische Sphäre. Fund. Math., 20:177-190, 1933.
5. [Bou85] J. Bourgain. On lipschitz embedding of finite metric spaces into hilbert space. Isreal Journal of Mathematics, 52:46-52, 1985.
6. [B0̌3] M Bǎdoiu. Approximation algorithm for embedding metrics into a two-dimensional space. 14th Annual ACM-SIAM Symposium on Discrete Algorithms, 2003.
7. [Dha04] Kedar Dhamdhere. Approximating additive distortion of embeddings into line metrics. 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), 2004.
8. [FCKW93] M. Farach-Colton, S. Kannan, and T. Warnow. A robust model for finding optimal evolutionary tree. Proceedings of the Symposium on Theory of Computing, 1993.
9. [Fei00] U. Feige. Approximating the bandwidth via volume respecting embeddings. Journal of Computer and System Sciences, 60(3):510-539, 2000.
10. [Gup00] Anupam Gupta. Improved bandwidth approximation for trees. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2000.
11. [HIL98] J. Hastad, L. Ivansson, and J. Lagergren. Fitting points on the real line and its application to rh mapping. Lecture Notes in Computer Science, 1461:465-467, 1998.
12. [Ind01] P. Indyk. Tutorial: Algorithmic applications of low-distortion geometric embeddings. Proceedings of the Symposium on Foundations of Computer Science, 2001.
13. [Iva00] L. Ivansson. Computational aspects of radiation hybrid. Doctoral Dissertation, Department of Numerical Analysis and Computer Science, Royal Institute of Technology, 2000.
14. [Kir34] M. D. Kirszbraun. Über die zusammenziehenden und lipschitzschen Transformationen. Fund. Math., 22:77-108, 1934.
15. [KRS04] C. Kenyon, Y. Rabani, and A. Sinclair. Low distortion maps between point sets. Proceedings of the Symposium on Theory of Computing, 2004. to appear.
16. [Kru64a] J.B. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29:1-27, 1964.
17. [Kru64b] J.B. Kruskal. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29:115-129, 1964.
18. [LLR94] N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Proceedings of 35th Annual IEEE Symposium on Foundations of Computer Science, pages 577-591, 1994.
19. [LN] J. R. Lee and A. Naor. Absolute lipschitz extendability. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, to appear.
20. [Mat90] J. Matoušek. Bi-lipschitz embeddings into low-dimensional euclidean spaces. Comment. Math. Univ. Carolinae, 31:589-600, 1990.
21. [Mat96] J. Matoušek. On the distortion required for embedding finite metric spaces into normed spaces. Israel Journal of Mathematics, 93:333-344, 1996.
22. [Sax80] J. B. Saxe. Dynamic-programming algorithms for recognizing small-bandwidth graphs in polynomial time. SIAM J. Algebraic Discrete Methods, 1:363-369, 1980.
23. [She62a] R. N. Shepard. The analysis of proximities: Multi-dimensional scaling with an unknown distance function 1. Psychometrika, 27:125-140, 1962.
24. [She62b] R. N. Shepard. The analysis of proximities: Multi-dimensional scaling with an unknown distance function 2. Psychometrika, 27:216-246, 1962.
25. [Wor] Working Group on Algorithms for Multidimensional Scaling. Algorithms for multidimensional scaling. http://dimacs.rutgers.edu/Workshops/ Algorithms/.