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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10172783%21RIV14-MSM-11320___
rdf:type
skos:Concept n13:Vysledek
rdfs:seeAlso
http://arxiv.org/abs/1101.0767
dcterms: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.
dcterms:title
The determinant bound for discrepancy is almost tight The determinant bound for discrepancy is almost tight
skos:prefLabel
The determinant bound for discrepancy is almost tight The determinant bound for discrepancy is almost tight
skos:notation
RIV/00216208:11320/13:10172783!RIV14-MSM-11320___
n13:predkladatel
n14:orjk%3A11320
n3:aktivita
n16:I
n3:aktivity
I
n3:cisloPeriodika
2
n3:dodaniDat
n8:2014
n3:domaciTvurceVysledku
n18:3374041
n3:druhVysledku
n10:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
68809
n3:idVysledku
RIV/00216208:11320/13:10172783
n3:jazykVysledku
n4:eng
n3:klicovaSlova
low-discrepancy colorings; incidence matrix; determinant bound; discrepancy
n3:klicoveSlovo
n5:incidence%20matrix n5:discrepancy n5:low-discrepancy%20colorings n5:determinant%20bound
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[F7CD241F98A5]
n3:nazevZdroje
Proceedings of the American Mathematical Society
n3:obor
n20:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
1
n3:rokUplatneniVysledku
n8:2013
n3:svazekPeriodika
141
n3:tvurceVysledku
Matoušek, Jiří
n3:wos
000326515600009
s:issn
0002-9939
s:numberOfPages
10
n12:doi
10.1090/S0002-9939-2012-11334-6
n19:organizacniJednotka
11320