Miklos Ajtai, Ravi Kumar, D. Sivakumar  Home/Search
Context Related
| ibm.com/cs/people/siva/papers/svp.ps Cached: PS.gz PS PDF This document uses CoBlitz to cache paper downloads. If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
Image Update HelpPS.gz PS PDF From: ibm.com/cs/people/siva/papers (more) (Enter author homepages) |
Rate this article:      (best)Comment on this article |
Abstract: We present a randomized 2 O(n) time algorithm to compute the shortest non-zero vector in an n-dimensional rational lattice. The best known time upper bound for this problem was 2 O(n log n) first given by Kannan [6] in 1983. We obtain several consequences of this algorithm for related problems on lattices and codes, including an improvement for polynomial time approximations to the shortest vector problem. In this improvement we gain a factor of log log n in the exponent of the... (Update)
Similar documents based on text: More All
0.9: A Note on the Shortest Lattice Vector Problem - Kumar, Sivakumar (1999) (Correct)
0.9: A Relation of Primal-Dual Lattices and the Complexity of.. - Jin-Yi Cai (1998) (Correct)
0.8: A new transference theorem and applications to Ajtai's connection.. - Cai (1998) (Correct)
BibTeX entry: (Update)
M. Ajtai, R. Kumar, and D. Sivakumar. A sieve algorithm for the shortest lattice vector problem. In Proc. 33rd STOC, pages 601--610. ACM, 2001. http://citeseer.ist.psu.edu/ajtai01sieve.html More
@inproceedings{ ajtai01sieve,
author = "Miklos Ajtai and Ravi Kumar and D. Sivakumar",
title = "A sieve algorithm for the shortest lattice vector problem",
booktitle = "{ACM} Symposium on Theory of Computing",
pages = "601-610",
year = "2001",
url = "citeseer.ist.psu.edu/ajtai01sieve.html" }
Citations (may not include all citations):227 Factoring polynomials with rational coefficients (context) - Lenstra, Lenstra et al. - 1982
84 Generating hard instances of lattice problems (context) - Ajtai - 1996
49 Minkowski's convex body theorem and integer programming (context) - Kannan
44 The shortest vector problem in L 2 is NP-hard for randomized.. (context) - Ajtai - 1998
33 An Algorithmic Theory of Numbers (context) - Lov'asz - 1986
30 The shortest vector in a lattice is hard to approximate to w.. - Micciancio - 1998
16 Algorithms to construct Minkowski reduced and Hermite reduce.. (context) - Helfrich - 1985
15 Another NP-complete partition problem and the complexity of .. (context) - Boas - 1981
7 Finding the closest lattice vector when it's unusually close - Klein - 2000
1 On polynomial approximations to the shortest lattice vector .. - Kumar, Sivakumar - 2001
1 and H. Wasserman. Noise-tolerant learning, the parity proble.. (context) - Blum, Kalai - 2000
1 A Some Technical Lemmas Lemma 14 There is a c (context) - Schnorr, of et al. - 1987
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.almaden.ibm.com/cs/people/siva/papers.html): More
Roundness Estimation Via Random Sampling - Kumar, Sivakumar (1999) (Correct)
Proofs, Codes, and Polynomial-Time Reducibilities - Kumar, Sivakumar (Correct)
Constant Depth Circuits and the Lutz Hypothesis - Cai, Sivakumar, Strauss (Correct)
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC