Lower bounds for local monotonicity reconstruction from transitive-closure spanners

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dc.contributor.authorBhattacharyya Arnabko
dc.contributor.authorGrigorescu Elenako
dc.contributor.authorJha Madhavko
dc.contributor.authorJung, Kyominko
dc.contributor.authorRaskhodnikova Sofyako
dc.contributor.authorWoodruff David P.ko
dc.date.accessioned2013-03-28T09:02:57Z-
dc.date.available2013-03-28T09:02:57Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2010-09-01-
dc.identifier.citation13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010, pp.448 - 461-
dc.identifier.issn0302-9743-
dc.identifier.urihttp://hdl.handle.net/10203/164347-
dc.description.abstractGiven 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, E-H) 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 reconstractors. 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](d) -> R, can quickly evaluate a related function g : [m](d) -> 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.-
dc.languageEnglish-
dc.publisherRANDOM-
dc.titleLower bounds for local monotonicity reconstruction from transitive-closure spanners-
dc.typeConference-
dc.identifier.wosid000284820600034-
dc.identifier.scopusid2-s2.0-78149304714-
dc.type.rimsCONF-
dc.citation.beginningpage448-
dc.citation.endingpage461-
dc.citation.publicationname13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010-
dc.identifier.conferencecountrySP-
dc.embargo.liftdate9999-12-31-
dc.embargo.terms9999-12-31-
dc.contributor.localauthorJung, Kyomin-
dc.contributor.nonIdAuthorBhattacharyya Arnab-
dc.contributor.nonIdAuthorGrigorescu Elena-
dc.contributor.nonIdAuthorJha Madhav-
dc.contributor.nonIdAuthorRaskhodnikova Sofya-
dc.contributor.nonIdAuthorWoodruff David P.-
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