Euclidean sections of ℓ1N with sublinear randomness and error-correction over the reals

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5171 LNCS, Issue , 2008, Pages 444-454

  Guruswami, Venkatesan ^a,b   Lee, James R ^a   Wigderson, Avi ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL OP-TIMIZATION PROBLEM; EUCLIDEAN;

COMBINATORIAL MATHEMATICS; COMBINATORIAL OPTIMIZATION; LEARNING SYSTEMS; OPTIMIZATION; POLYNOMIAL APPROXIMATION;

APPROXIMATION ALGORITHMS;

EID: 51849090137     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-85363-3_35     Document Type: Conference Paper

References (23)

1. Artstein-Avidan, S., Milman, V.D.: Logarithmic reduction of the level of randomness in some probabilistic geometric constructions. J. Funct. Anal. 235(1), 297-329 (2006)
2. Alon, N.: Personal communication (2008)
3. Candes, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inform. Theory 51(12), 4203-4215 (2005)
4. Donoho, D.L.: Compressed sensing. IEEE Transactions on Information Theory 52, 1289-1306 (2006)
5. Figiel, T., Lindenstrauss, J., Milman, V.D.: The dimension of almost spherical sections of convex bodies. Acta Math. 139(1-2), 53-94 (1977)
6. Garnaev, A., Gluskin, E.D.: The widths of Euclidean balls. Doklady An. SSSR. 277, 1048-1052 (1984)
7. Guruswami, V., Indyk, P.: Linear-time encodable/decodable codes with near-optimal rate. IEEE Trans. Inform. Theory 51(10), 3393-3400 (2005)
8. 1 via expander codes. In: SODA 2008: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics, pp. 353-362 (2008)
9. Hoory, S., Linial, N., Wigderson, A.: Expander graphs and their applications. Bull. Amer. Math. Soc. (N.S.) 43(4), 439-561 (2006)
10. Indyk, P.: Stable distributions, pseudorandom generators, embeddings, and data stream computation. Journal of the ACM 53(3), 307-323 (2006)
11. 1. In: Proceedings of the 39th Annual ACM Symposium on the Theory of Computing, pp. 615-620 (2007)
12. p. In: Handbook of the geometry of Banach spaces, vol. I, pp. 837-870. North-Holland, Amsterdam (2001)
13. Kashin, B.S.: The widths of certain finite-dimensional sets and classes of smooth functions. Izv. Akad. Nauk SSSR Ser. Mat. 41(2), 334-351, 478 (1977)
14. Kashin, B.S., Temlyakov, V.N.: A remark on compressed sensing (2007), http://www.dsp.ece.rice.edu/cs/KT2007.pdf
15. Lubotzky, A., Phillips, R., Sarnak, P.: Ramanujan graphs. Combinatorica 8(3), 261-277 (1988)
16. Lovett, S., Sodin, S.: Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits. Electronic Colloquium on Computational Complexity, Report TR07-012 (2007)
17. Milman, V.: Topics in asymptotic geometric analysis. Geom. Funct. Anal., 792-815 (2000) (Special Volume, Part II); GAFA 2000 (Tel Aviv, 1999)
18. Schütt, C: Entropy numbers of diagonal operators between symmetric Banach spaces. J. Approx. Theory 40(2), 121-128 (1984)
19. Sipser, M., Spielman, D.A.: Expander codes. IEEE Trans. Inform. Theory 42(6, part 1), 1710-1722 (1996) (Codes and complexity)
20. Szarek, S.: Convexity, complexity, and high dimensions. In: International Congress of Mathematicians, vol. II, pp. 1599-1621. Eur. Math. Soc, Zürich (2006)
21. Tanner, R.M.: A recursive approach to low complexity codes. IEEE Transactions on Information Theory 27(5), 533-547 (1981)
22. Xu, W., Hassibi, B.: Efficient compressive sensing with determinstic guarantees using expander graphs. In: IEEE Information Theory Workshop (September 2007)
23. Zémor, G.: On expander codes. IEEE Transactions on Information Theory 47(2), 835-837 (2001)