About: Simplifying inclusion-exclusion formulas

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Simplifying inclusion-exclusion formulas Goto Sponge NotDistinct Permalink

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

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.springer.com/chapter/10.1007/978-88-7642-475-5_88
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. (en)
Title	Simplifying inclusion-exclusion formulas Simplifying inclusion-exclusion formulas (en)
skos:prefLabel	Simplifying inclusion-exclusion formulas Simplifying inclusion-exclusion formulas (en)
skos:notation	RIV/00216208:11320/13:10190922!RIV14-GA0-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(GEGIG/11/E023), S
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Paták, Pavel Matoušek, Jiří Tancer, Martin Safernová, Zuzana
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
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	105136
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10190922
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Venn diagram; inclusion - exclusion formula (en)
http://linked.open.../riv/klicoveSlovo	Venn diagram inclusion
http://linked.open...ontrolniKodProRIV	[73AC8304DEA9]
http://linked.open...v/mistoKonaniAkce	Pisa
http://linked.open...i/riv/mistoVydani	Pisa
http://linked.open...i/riv/nazevZdroje	The Seventh European Conference on Combinatorics, Graph Theory and Applications; EuroComb 2013
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	4 (xsd:int)
http://linked.open...cetTvurcuVysledku	5 (xsd:int)
http://linked.open...vavai/riv/projekt	Graph Drawings and Representations
http://linked.open...UplatneniVysledku	2013
http://linked.open...iv/tvurceVysledku	Matoušek, Jiří Tancer, Martin Safernová, Zuzana Goaoc, Xavier Paták, Pavel
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2013-09-09 (xsd:date)
number of pages	7 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-88-7642-475-5_88
http://purl.org/ne...btex#hasPublisher	Scuola Normale Superiore
https://schema.org/isbn	978-88-7642-474-8
http://localhost/t...ganizacniJednotka	11320

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software