On the distortion required for embedding finite metric spaces into normed spaces

Israel Journal of Mathematics

Volumn 93, Issue , 1996, Pages 333-344

  Matoušek, Jiří ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030445230     PISSN: 00212172     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02761110     Document Type: Article

References (18)

1. N. Alon, P. Frankl and V. Rödl, Geometrical realization of set systems and probabilistic communication complexity, Proc. 26th IEEE Symposium on Foundations of Computer Science, 1985, pp. 277-280.
2. J. Arias-de-Reyna and L. Rodríguez-Piazza, Finite metric spaces needing high dimension for Lipschitz embeddings in Banach spaces, Israel Journal of Mathematics 79 (1992), 103-113.
3. C. T. Benson, Minimal regular graphs of girth eight and twelve, Canadian Journal of Mathematics 18 (1966), 1091-1094.
4. N. Biggs, Algebraic Graph Theory, Cambridge University Press, 1974.
5. B. Bollobás, Extremal Graph Theory, Academic Press, London, 1978.
6. J. Bourgain, On Lipschitz embedding of finite metric spaces in Hilbert space, Israel Journal of Mathematics 52 (1985), 46-52.
7. J. Bourgain, The metrical interpretation of superreflexivity in Banach spaces, Israel Journal of Mathematics 56 (1986), 222-230.
8. J. Bourgain, V. Milman and H. Wolfson, On type of metric spaces, Transactions of the American Mathematical Society 294 (1986), 295-317.
9. B. Grünbaum, Convex Polytopes, John Wiley & Sons, London, 1967.
10. W. Johnson and J. Lindenstrauss, Extensions of Lipschitz maps into a Hilbert space, Contemporary Mathematics 26 (Conference in Modern Analysis and Probability), American Mathematical Society, 1984, pp. 189-206.
11. W. Johnson, J. Lindenstrauss and G. Schechtman, On Lipschitz embedding of finite metric spaces in low dimensional normed spaces, in Geometrical Aspects of Functional Analysis (J. Lindenstrauss and V. D. Milman, eds.), Lecture Notes in Mathematics 1267, Springer-Verlag, Berlin-Heidelberg, 1987.
12. N. Linial, E. London and Yu. Rabinovich, The geometry of graphs and some of its algorithmic applications, Proceedings of the 35th IEEE Symposium on Foundations of Computer Science (1994), pp. 577-591. Journal version: Combinatorica 15 (1995), 215-245.
13. N. Linial, E. London and Yu. Rabinovich, The geometry of graphs and some of its algorithmic applications, Proceedings of the 35th IEEE Symposium on Foundations of Computer Science (1994), pp. 577-591. Journal version: Combinatorica 15 (1995), 215-245.
14. A. Lubotzky, R. Phillips and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261-277.
15. J. Matoušek, Bi-Lipschitz embeddings into low-dimensional Euclidean spaces, Commentationes Mathematicae Universitatis Carolinae 31 (1990), 589-600.
16. J. Matoušek, Note on bi-Lipschitz embeddings into normed spaces, Commentationes Mathematicae Universitatis Carolinae 33 (1992), 51-55.
17. J. Milnor, On the betti numbers of real algebraic varieties, Proceedings of the American Mathematical Society 15 (1964), 275-280.
18. R. Thom, Sur l'homologie des variétés algébriques reélles, in Differential and Combinatorial Topology (S. S. Cairns, ed.), Princeton Univ. Press, 1965.