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Bounded Independence vs. Moduli
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-5379-345X
2016 (English)In: Leibniz International Proceedings in Informatics, LIPIcs, Dagstuhl Publishing , 2016Conference paper (Refereed)
Abstract [en]

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 Sm := {x 2 {0, 1}n : Σi xi ≡ 0 mod m}, where m is any integer. We show that Ω(n/m2 logm) ≤ 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 Sm. For any fixed odd m there is k ≥ (1-Ω(1))n such that any k-wise uniform distribution lands in Sm with probability exponentially close to |Sm|/2n; and this result is false for any even m.

Place, publisher, year, edition, pages
Dagstuhl Publishing , 2016.
Keyword [en]
Bounded independence, Modulus, Approximation algorithms, Combinatorial optimization, Optimization, Random processes, Uniform distribution, Probability distributions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-202890DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.24ScopusID: 2-s2.0-84990829261ISBN: 9783959770187 OAI: oai:DiVA.org:kth-202890DiVA: diva2:1079671
Conference
19th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2016 and the 20th International Workshop on Randomization and Computation, RANDOM 2016, 7 September 2016 through 9 September 2016
Note

QC 20170309

Available from: 2017-03-09 Created: 2017-03-09 Last updated: 2017-03-09Bibliographically approved

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