Randomly Supported Independence and Resistance
2009 (English)In: STOC'09: PROCEEDINGS OF THE 2009 ACM SYMPOSIUM ON THEORY OF COMPUTING, NEW YORK: ASSOC COMPUTING MACHINERY , 2009, 483-492 p.Conference paper (Refereed)
We prove that for any positive integer k, there is a constant C-k such that a randomly selected set of c(k)n(k) log n Boolean vectors with high probability supports a balanced k-wise independent distribution. In the case of k <= 2 a more elaborate argument, gives the strong-er bound ckn(k). Using a recent, result. by Austrin and Mossel this shows that a predicate on t, bits. Chosen at, random among predicates accepting c(2)t(2) input, vectors, is, assuming the Unique Games Conjecture, likely to be approximation resistant. These result's are close to tight,: we show that there are other constants, c(k)(1), such that a randomly selected set of points is unlikely to support a balanced k-wise. independent distribution and for some c > 0, a random predicate accepting ct(2)/log t input, vectors is is non-trivially approximable with high probability. In a different application of the result of Austrin and Mossel we prove that, again assuming the Unique Games Conjecture, any predicate on t bits accepting at least (32/33) - 2(t) inputs is approximation resistant. The results extend front the Boolean domain to larger finite domains.
Place, publisher, year, edition, pages
NEW YORK: ASSOC COMPUTING MACHINERY , 2009. 483-492 p.
IdentifiersURN: urn:nbn:se:kth:diva-30772DOI: 10.1145/1536414.1536481ISI: 000268182000054ScopusID: 2-s2.0-70350701826ISBN: 978-1-60558-613-7OAI: oai:DiVA.org:kth-30772DiVA: diva2:404749
41st Annual ACM Symposium on Theory of Computing Bethesda, MD, MAY 31-JUN 02, 2009
QC 201103182011-03-182011-03-042016-04-27Bibliographically approved