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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10190922%21RIV14-GA0-11320___
rdf:type
n3:Vysledek skos:Concept
rdfs:seeAlso
http://link.springer.com/chapter/10.1007/978-88-7642-475-5_88
dcterms:description
Let F = (F 1, F 2, ..., F n) be a family of n sets on a ground set S, such as a family of balls in R d. For every finite measure μ on S, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that μ (F 1 UNION F 2 UNION ...UNION F n) = N-ARY SUMMATIONI:oNOT EQUAL TOSUBSET OF OR EQUAL TO  [n] (MINUS SIGN 1)|I|+1μ(INTERSECTIONi ELEMENT OFIF i); that is, the measure of the union is expressed using measures of various intersections. The number of terms in this formula is exponential in n, and a significant amount of research, originating in applied areas, has been devoted to constructing simpler formulas for particular families F. We provide an upper bound valid for an arbitrary F: we show that every system F of n sets with m nonempty fields in the Venn diagram admits an inclusion-exclusion formula with m O (log2 n) terms and with +-1 coefficients, and that such a formula can be computed in m O (log2 n) expected time. Let F = (F 1, F 2, ..., F n) be a family of n sets on a ground set S, such as a family of balls in R d. For every finite measure μ on S, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that μ (F 1 UNION F 2 UNION ...UNION F n) = N-ARY SUMMATIONI:oNOT EQUAL TOSUBSET OF OR EQUAL TO  [n] (MINUS SIGN 1)|I|+1μ(INTERSECTIONi ELEMENT OFIF i); that is, the measure of the union is expressed using measures of various intersections. The number of terms in this formula is exponential in n, and a significant amount of research, originating in applied areas, has been devoted to constructing simpler formulas for particular families F. We provide an upper bound valid for an arbitrary F: we show that every system F of n sets with m nonempty fields in the Venn diagram admits an inclusion-exclusion formula with m O (log2 n) terms and with +-1 coefficients, and that such a formula can be computed in m O (log2 n) expected time.
dcterms:title
Simplifying inclusion-exclusion formulas Simplifying inclusion-exclusion formulas
skos:prefLabel
Simplifying inclusion-exclusion formulas Simplifying inclusion-exclusion formulas
skos:notation
RIV/00216208:11320/13:10190922!RIV14-GA0-11320___
n3:predkladatel
n14:orjk%3A11320
n4:aktivita
n11:S n11:P
n4:aktivity
P(GEGIG/11/E023), S
n4:dodaniDat
n18:2014
n4:domaciTvurceVysledku
n9:5278880 n9:3374041 n9:2414767 n9:1065858
n4:druhVysledku
n13:D
n4:duvernostUdaju
n23:S
n4:entitaPredkladatele
n21:predkladatel
n4:idSjednocenehoVysledku
105136
n4:idVysledku
RIV/00216208:11320/13:10190922
n4:jazykVysledku
n19:eng
n4:klicovaSlova
Venn diagram; inclusion - exclusion formula
n4:klicoveSlovo
n16:inclusion n16:Venn%20diagram
n4:kontrolniKodProRIV
[73AC8304DEA9]
n4:mistoKonaniAkce
Pisa
n4:mistoVydani
Pisa
n4:nazevZdroje
The Seventh European Conference on Combinatorics, Graph Theory and Applications; EuroComb 2013
n4:obor
n20:BA
n4:pocetDomacichTvurcuVysledku
4
n4:pocetTvurcuVysledku
5
n4:projekt
n24:GEGIG%2F11%2FE023
n4:rokUplatneniVysledku
n18:2013
n4:tvurceVysledku
Goaoc, Xavier Tancer, Martin Safernová, Zuzana Matoušek, Jiří Paták, Pavel
n4:typAkce
n5:WRD
n4:zahajeniAkce
2013-09-09+02:00
s:numberOfPages
7
n7:doi
10.1007/978-88-7642-475-5_88
n8:hasPublisher
Scuola Normale Superiore
n15:isbn
978-88-7642-474-8
n10:organizacniJednotka
11320