Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions

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dc.contributor.authorChoi, SSko
dc.contributor.authorJung, Kyominko
dc.contributor.authorKim, JHko
dc.date.accessioned2013-03-11T00:08:35Z-
dc.date.available2013-03-11T00:08:35Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2011-11-
dc.identifier.citationJOURNAL OF COMPUTER AND SYSTEM SCIENCES, v.77, pp.1039 - 1053-
dc.identifier.issn0022-0000-
dc.identifier.urihttp://hdl.handle.net/10203/97753-
dc.description.abstractA k-bounded pseudo-Boolean function is a real-valued function on {0, 1}(n) that can be expressed as a sum of functions depending on at most k input bits. The k-bounded functions play an important role in a number of areas including molecular biology, biophysics, and evolutionary computation. We consider the problem of finding the Fourier coefficients of k-bounded functions, or equivalently, finding the coefficients of multilinear polynomials on {-1, 1}(n) of degree k or less. Given a k-bounded function f with m non-zero Fourier coefficients for constant k, we present a randomized algorithm to find the Fourier coefficients of f with high probability in O(m logn) function evaluations. The best known upper bound was O(lambda(n, m)m log n), where lambda(n, m) is between n(1/2) and n depending on m. Our bound improves the previous bound by a factor of Omega(n(1/2)). It is almost tight with respect to the lower bound Omega(mlogn/logm). In the process, we also consider the problem of finding k-bounded hypergraphs with a certain type of queries under an oracle with one-sided error. The problem is of self interest and we give an optimal algorithm for the problem. (C) 2010 Elsevier Inc. All rights reserved.-
dc.languageEnglish-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.subjectEFFICIENT-
dc.subjectSPECTRUM-
dc.subjectGRAPHS-
dc.subjectDNF-
dc.titleAlmost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions-
dc.typeArticle-
dc.identifier.wosid000294833400007-
dc.identifier.scopusid2-s2.0-80052341376-
dc.type.rimsART-
dc.citation.volume77-
dc.citation.beginningpage1039-
dc.citation.endingpage1053-
dc.citation.publicationnameJOURNAL OF COMPUTER AND SYSTEM SCIENCES-
dc.contributor.localauthorJung, Kyomin-
dc.contributor.nonIdAuthorChoi, SS-
dc.contributor.nonIdAuthorKim, JH-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorPseudo-Boolean function-
dc.subject.keywordAuthorFourier coefficients-
dc.subject.keywordAuthorGraph finding-
dc.subject.keywordAuthorLearning polynomials-
dc.subject.keywordAuthorLinkage discovery-
dc.subject.keywordAuthorWalsh analysis-
dc.subject.keywordPlusEFFICIENT-
dc.subject.keywordPlusSPECTRUM-
dc.subject.keywordPlusGRAPHS-
dc.subject.keywordPlusDNF-
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