Low-distortion embeddings of general metrics into the line

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2005, Pages 225-233

  Bǎdoiu, Mihai ^a   Chuzhoy, Julia ^a   Indyk, Piotr ^a   Sidiropoulos, Anastasios ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Approximation algorithms; Metric embeddings

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SCIENCE; CONFORMAL MAPPING; METRIC SYSTEM; POLYNOMIALS; TREES (MATHEMATICS);

APPROXIMATION ALGORITHMS; EMBEDDING PROBLEMS; METRIC EMBEDDINGS; METRIC SPACES;

EMBEDDED SYSTEMS;

EID: 33748074187     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1060590.1060624     Document Type: Conference Paper

References (21)

1. 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. M Bǎdoiu. Approximation algorithm for embedding metrics into a two-dimensional space. 14th Annual ACM-SIAM Symposium on Discrete Algorithms, 2003.
3. M. Bǎdoiu, E. Demaine, M. Hajiaghai, and P. Indyk. Embeddings with extra information. Proceedings of the ACM Symposium on Computational Geometry, 2004.
4. M. Bǎdoiu, K. Dhamdhere, A. Gupta, Y. Rabinovich, H. Raecke, R. Ravi, and A. Sidiropoulos. Approximation algorithms for low-distortion embeddings into low-dimensional spaces. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2005.
5. M. Bǎdoiu, P. Indyk, and A. Sidiropoulos. A constant-factor approximation algorithm for embedding unweighted graphs into trees. AI Lab Technical Memo AIM-2004-015, 2004.
6. K. Dhamdhere. Approximating additive distortion of line embeddings. Proceedings of RANDOM-APPROX, 2004.
7. K. Dhamdhere, A. Gupta, and R. Ravi. Approximating average distortion for embeddings into line. Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), 2004.
8. J. Dunagan and S. Vempala. On euclidean embeddings and bandwidth minimization. Proceedings of the 5th Workshop on Randomization and Approximation, 2001.
9. Y. Emek and D. Peleg. Approximating minimum max-stretch spanning trees on unweighted graphs. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, 2004.
10. M. Farach-Colton, S. Kannan, and T. Warnow. A robust model for finding optimal evolutionary tree. Annual ACM Symposium on Theory of Computing, 1993.
11. U. Feige. Approximating the bandwidth via volume respecting embeddings. Journal of Computer and System Sciences, 60(3):510-539, 2000.
12. 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.
13. P. Indyk. Tutorial: Algorithmic applications of low-distortion geometric embeddings. Annual Symposium on Foundations of Computer Science, 2001.
14. C. Kenyon, Y. Rabani, and A. Sinclair. Low distortion maps between point sets. Annual ACM Symposium on Theory of Computing, 2004.
15. N. Linial. Finite metric spaces - combinatorics, geometry and algorithms. Proceedings of the International Congress of Mathematicians III, pages 573-586, 2002.
16. 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.
17. J. Matoušek. Bi-lipschitz embeddings into low-dimensional euclidean spaces. Comment. Math. Univ. Carolinae, 31:589-600, 1990.
18. MDS: Working Group on Algorithms for Multidimensional Scaling. Algorithms for multidimensional scaling. DIMACS Web Page.
19. C. Papadimitriou and S. Safra. The complexity of low-distortion embeddings between point sets. Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pages 112-118, 2005.
20. J. B. Tenenbaum, V. de Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. http://isomap.Stanford.edu/.
21. W. Unger. The complexity of the approximation of the bandwidth problem. Annual Symposium on Foundations of Computer Science, 1998.