DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bhattacharyya, A | ko |
dc.contributor.author | Grigorescu, E | ko |
dc.contributor.author | Jha, M | ko |
dc.contributor.author | Jung, Kyo-Min | ko |
dc.contributor.author | Raskhodnikova, S | ko |
dc.contributor.author | Woodruff, DP | ko |
dc.date.accessioned | 2013-03-09T22:21:19Z | - |
dc.date.available | 2013-03-09T22:21:19Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | LECTURE NOTES IN COMPUTER SCIENCE (INCLUDING SUBSERIES LECTURE NOTES IN ARTIFICIAL INTELLIGENCE AND LECTURE NOTES IN BIOINFORMATICS), v.6302, pp.448 - 461 | - |
dc.identifier.issn | 0302-9743 | - |
dc.identifier.uri | http://hdl.handle.net/10203/97651 | - |
dc.description.abstract | Given a directed graph G=(V,E) and an integer k≥1, a k-transitive-closure-spanner ( k-TC-spanner) of G is a directed graph H=(V, EH ) that has (1) the same transitive-closure as G and (2) diameter at most k. Transitive-closure spanners are a common abstraction for applications in access control, property testing and data structures. We show a connection between 2-TC-spanners and local monotonicity reconstructors. A local monotonicity reconstructor, introduced by Saks and Seshadhri (SIAM Journal on Computing, 2010), is a randomized algorithm that, given access to an oracle for an almost monotone function f : [m] → ℝ, can quickly evaluate a related function g : [m] → ℝ which is guaranteed to be monotone. Furthermore, the reconstructor can be implemented in a distributed manner. We show that an efficient local monotonicity reconstructor implies a sparse 2-TC-spanner of the directed hypergrid (hypercube), providing a new technique for proving lower bounds for local monotonicity reconstructors. Our connection is, in fact, more general: an efficient local monotonicity reconstructor for functions on any partially ordered set (poset) implies a sparse 2-TC-spanner of the directed acyclic graph corresponding to the poset. We present tight upper and lower bounds on the size of the sparsest 2-TC-spanners of the directed hypercube and hypergrid. These bounds imply tighter lower bounds for local monotonicity reconstructors that nearly match the known upper bounds. © 2010 Springer-Verlag. | - |
dc.language | English | - |
dc.publisher | SPRINGER-VERLAG BERLIN | - |
dc.title | Lower bounds for local monotonicity reconstruction from transitive-closure spanners | - |
dc.type | Article | - |
dc.identifier.scopusid | 2-s2.0-78149304714 | - |
dc.type.rims | ART | - |
dc.citation.volume | 6302 | - |
dc.citation.beginningpage | 448 | - |
dc.citation.endingpage | 461 | - |
dc.citation.publicationname | LECTURE NOTES IN COMPUTER SCIENCE (INCLUDING SUBSERIES LECTURE NOTES IN ARTIFICIAL INTELLIGENCE AND LECTURE NOTES IN BIOINFORMATICS) | - |
dc.contributor.localauthor | Jung, Kyo-Min | - |
dc.contributor.nonIdAuthor | Bhattacharyya, A | - |
dc.contributor.nonIdAuthor | Grigorescu, E | - |
dc.contributor.nonIdAuthor | Jha, M | - |
dc.contributor.nonIdAuthor | Raskhodnikova, S | - |
dc.contributor.nonIdAuthor | Woodruff, DP | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Conference Paper | - |
dc.subject.keywordAuthor | Hypercube | - |
dc.subject.keywordAuthor | Hypergrid | - |
dc.subject.keywordAuthor | Monotone Functions | - |
dc.subject.keywordAuthor | Property Reconstruction | - |
dc.subject.keywordAuthor | Property Testing | - |
dc.subject.keywordAuthor | Spanners | - |
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