Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Boppana, Ravi; Håstad, Johan; Lee, Chin Ho; Viola, Emanuele http://www.dagstuhl.de/lipics License
when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-66475
URL:

; ; ;

Bounded Independence vs. Moduli

pdf-format:


Abstract

Let k = k(n) be the largest integer such that there exists a k-wise uniform distribution over {0,1}^n that is supported on the set S_m := {x in {0,1}^n: sum_i x_i equiv 0 mod m}, where m is any integer. We show that Omega(n/m^2 log m) <= k <= 2n/m + 2. For k = O(n/m) we also show that any k-wise uniform distribution puts probability mass at most 1/m + 1/100 over S_m. For any fixed odd m there is k \ge (1 - Omega(1))n such that any k-wise uniform distribution lands in S_m with probability exponentially close to |S_m|/2^n; and this result is false for any even m.

BibTeX - Entry

@InProceedings{boppana_et_al:LIPIcs:2016:6647,
  author =	{Ravi Boppana and Johan Håstad and Chin Ho Lee and Emanuele Viola},
  title =	{{Bounded Independence vs. Moduli}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{24:1--24:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6647},
  URN =		{urn:nbn:de:0030-drops-66475},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.24},
  annote =	{Keywords: Bounded independence, Modulus}
}

Keywords: Bounded independence, Modulus
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)
Issue date: 2016
Date of publication: 2016


DROPS-Home | Fulltext Search | Imprint Published by LZI