DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bhattacharyya, Arnab | ko |
dc.contributor.author | Grigorescu, Elena | ko |
dc.contributor.author | Jha, Madhav | ko |
dc.contributor.author | Jung, Kyomin | ko |
dc.contributor.author | Raskhodnikova, Sofya | ko |
dc.contributor.author | Woodruff, David P. | ko |
dc.date.accessioned | 2013-03-12T16:29:32Z | - |
dc.date.available | 2013-03-12T16:29:32Z | - |
dc.date.created | 2012-07-04 | - |
dc.date.created | 2012-07-04 | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | SIAM JOURNAL ON DISCRETE MATHEMATICS, v.26, no.2, pp.618 - 646 | - |
dc.identifier.issn | 0895-4801 | - |
dc.identifier.uri | http://hdl.handle.net/10203/102872 | - |
dc.description.abstract | Given a directed graph G = (V, E) and an integer k >= 1, a k-transitive-closurespanner (k-TC-spanner) of G is a directed graph H = (V, E-H) that has (1) the same transitive-closure as G and (2) diameter at most k. Transitive-closure spanners are used in access control, property testing and data structures. We show a connection between 2-TC-spanners and local monotonicity filters. A local monotonicity filter, introduced by Saks and Seshadhri [SIAM J. Comput., pp. 2897-2926], is a randomized algorithm that, given access to an oracle for an almost monotone function f : {1, 2,...,m}(d)-> R, can quickly evaluate a related function g : {1, 2,..., m}(d)-> R which is guaranteed to be monotone. Furthermore, the filter can be implemented in a distributed manner. We show that an efficient local monotonicity filter implies a sparse 2-TC-spanner of the directed hypergrid, providing a new technique for proving lower bounds for local monotonicity filters. Our connection is, in fact, more general: an efficient local monotonicity filter 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 nearly tight upper and lower bounds on the size of the sparsest 2-TC-spanners of the directed hypercube and hypergrid. These bounds imply stronger lower bounds for local monotonicity filters that nearly match the upper bounds of Saks and Seshadhri. | - |
dc.language | English | - |
dc.publisher | SIAM PUBLICATIONS | - |
dc.subject | APPROXIMATE DISTANCE ORACLES | - |
dc.subject | CIRCUITS | - |
dc.subject | STRETCH | - |
dc.subject | GRAPHS | - |
dc.subject | PATHS | - |
dc.subject | TIME | - |
dc.title | LOWER BOUNDS FOR LOCAL MONOTONICITY RECONSTRUCTION FROM TRANSITIVE-CLOSURE SPANNERS | - |
dc.type | Article | - |
dc.identifier.wosid | 000305962300015 | - |
dc.identifier.scopusid | 2-s2.0-84865290100 | - |
dc.type.rims | ART | - |
dc.citation.volume | 26 | - |
dc.citation.issue | 2 | - |
dc.citation.beginningpage | 618 | - |
dc.citation.endingpage | 646 | - |
dc.citation.publicationname | SIAM JOURNAL ON DISCRETE MATHEMATICS | - |
dc.identifier.doi | 10.1137/100808186 | - |
dc.contributor.localauthor | Jung, Kyomin | - |
dc.contributor.nonIdAuthor | Bhattacharyya, Arnab | - |
dc.contributor.nonIdAuthor | Grigorescu, Elena | - |
dc.contributor.nonIdAuthor | Jha, Madhav | - |
dc.contributor.nonIdAuthor | Raskhodnikova, Sofya | - |
dc.contributor.nonIdAuthor | Woodruff, David P. | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | property testing | - |
dc.subject.keywordAuthor | property reconstruction | - |
dc.subject.keywordAuthor | monotone functions | - |
dc.subject.keywordAuthor | spanners | - |
dc.subject.keywordAuthor | hypercube | - |
dc.subject.keywordAuthor | hypergrid | - |
dc.subject.keywordPlus | APPROXIMATE DISTANCE ORACLES | - |
dc.subject.keywordPlus | CIRCUITS | - |
dc.subject.keywordPlus | STRETCH | - |
dc.subject.keywordPlus | GRAPHS | - |
dc.subject.keywordPlus | PATHS | - |
dc.subject.keywordPlus | TIME | - |
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