About: The determinant bound for discrepancy is almost tight

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://arxiv.org/abs/1101.0767
Description	In 1986 Lovasz, Spencer, and Vesztergombi proved a lower bound for the hereditary a discrepancy of a set system F in terms of determinants of square submatrices of the incidence matrix of F. As shown by an example of Hoffman, this bound can differ from herdisc(F) by a multiplicative factor of order almost log n, where n is the size of the ground set of F. We prove that it never differs by more than O((log n)^3/2), assuming \|F\| bounded by a polynomial in n. We also prove that if such an F is the union of t systems F_1, . . ., F_t, each of hereditary discrepancy at most D, then herdisc(F) \leq O(t^(1/2)(log n)^(3/2) D). For t = 2, this almost answers a question of Sos. The proof is based on a recent algorithmic result of Bansal, which computes low-discrepancy colorings using semidefinite programming. In 1986 Lovasz, Spencer, and Vesztergombi proved a lower bound for the hereditary a discrepancy of a set system F in terms of determinants of square submatrices of the incidence matrix of F. As shown by an example of Hoffman, this bound can differ from herdisc(F) by a multiplicative factor of order almost log n, where n is the size of the ground set of F. We prove that it never differs by more than O((log n)^3/2), assuming \|F\| bounded by a polynomial in n. We also prove that if such an F is the union of t systems F_1, . . ., F_t, each of hereditary discrepancy at most D, then herdisc(F) \leq O(t^(1/2)(log n)^(3/2) D). For t = 2, this almost answers a question of Sos. The proof is based on a recent algorithmic result of Bansal, which computes low-discrepancy colorings using semidefinite programming. (en)
Title	The determinant bound for discrepancy is almost tight The determinant bound for discrepancy is almost tight (en)
skos:prefLabel	The determinant bound for discrepancy is almost tight The determinant bound for discrepancy is almost tight (en)
skos:notation	RIV/00216208:11320/13:10172783!RIV14-MSM-11320___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Matoušek, Jiří
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	68809
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10172783
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	low-discrepancy colorings; incidence matrix; determinant bound; discrepancy (en)
http://linked.open.../riv/klicoveSlovo	incidence matrix determinant bound low-discrepancy colorings discrepancy
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[F7CD241F98A5]
http://linked.open...i/riv/nazevZdroje	Proceedings of the American Mathematical Society
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	141
http://linked.open...iv/tvurceVysledku	Matoušek, Jiří
http://linked.open...ain/vavai/riv/wos	000326515600009
issn	0002-9939
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1090/S0002-9939-2012-11334-6
http://localhost/t...ganizacniJednotka	11320

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