ALMOST EUCLIDEAN SUBSPACES OF l1N VIA EXPANDER CODES

被引：9

作者：

Guruswami, Venkatesan ^{[1
,2
]}

Lee, James R. ^{[2
]}

Razborov, Alexander ^{[3
,4
]}

机构：

[1] Carnegie Mellon Univ, Dept Comp Sci, Pittsburgh, PA 15213 USA

[2] Univ Washington, Dept Comp Sci & Engn, Seattle, WA 98195 USA

[3] Univ Chicago, Dept Comp Sci, Chicago, IL 60637 USA

[4] VA Steklov Math Inst, Moscow 117966, Russia

来源：

COMBINATORICA | 2010年 / 30卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

RANDOMNESS; EMBEDDINGS; SECTIONS; GRAPHS; FIELDS;

D O I：

10.1007/s00493-010-2463-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an explicit (in particular, deterministic polynomial time) construction of subspaces X subset of R-N of dimension (1-o(1))N such that for every x is an element of X, (log N)(-O(log log log N)) root N parallel to x parallel to(2) <= parallel to x parallel to(1) <= root N parallel to x parallel to(2). If we are allowed to use N-1/log log N <= N degrees((1)) random bits and dim(X) >= (1-eta)N for any fixed constant eta, the lower bound can be further improved to (log N)(-O(1))root N parallel to x parallel to(2).

引用

页码：47 / 68

页数：22

共 50 条

[1] Almost Euclidean subspaces of l1N via expander codes
Guruswami, Venkatesan
Lee, James R.
Razborov, Alexander
[J]. PROCEEDINGS OF THE NINETEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2008, : 353 - +
[2] Almost Euclidean subspaces of ℓ1N VIA expander codes
Venkatesan Guruswami
James R. Lee
Alexander Razborov
[J]. Combinatorica, 2010, 30 : 47 - 68
[3] Almost-Euclidean Subspaces of l1N via Tensor Products: A Simple Approach to Randomness Reduction
Indyk, Piotr
Szarek, Stanislaw
[J]. APPROXIMATION, RANDOMIZATION, AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES, 2010, 6302 : 632 - +
[4] EMBEDDING SUBSPACES OF L1 INTO L1N
TALAGRAND, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 108 (02) : 363 - 369
[5] Orthogonal almost locally minimal projections on l1n
Zippin, M
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2000, 115 (1) : 253 - 268
[6] ε-isometries in l1n
Vestfrid, Igor A.
[J]. AEQUATIONES MATHEMATICAE, 2024,
[7] EMBEDDING LPM INTO L1N
JOHNSON, WB
SCHECHTMAN, G
[J]. ACTA MATHEMATICA, 1982, 149 (1-2) : 71 - 85
[8] Euclidean Sections of l1N with Sublinear Randomness and Error-Correction over the Reals
Guruswami, Venkatesan
Lee, James R.
Wigderson, Avi
[J]. APPROXIMATION RANDOMIZATION AND COMBINATORIAL OPTIMIZATION: ALGORITHMS AND TECHNIQUES, PROCEEDINGS, 2008, 5171 : 444 - +
[9] Characterizations of l∞n and l1n and their stabilities
Martini, Horst
Wu, Senlin
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (02) : 688 - 702
[10] KASHINS ALMOST EUCLIDEAN ORTHOGONAL DECOMPOSITION OF L-N(1)
SZAREK, SJ
[J]. BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1978, 26 (08): : 691 - 694

← 1 2 3 4 5 →