Simplifying inclusion-exclusion formulas

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190922" target="_blank" >RIV/00216208:11320/13:10190922 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/chapter/10.1007/978-88-7642-475-5_88" target="_blank" >http://link.springer.com/chapter/10.1007/978-88-7642-475-5_88</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-88-7642-475-5_88" target="_blank" >10.1007/978-88-7642-475-5_88</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Simplifying inclusion-exclusion formulas

Popis výsledku v původním jazyce

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 ? on S, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that ? (F 1 UNION F 2 UNION...UNION F n) = N-ARY SUMMATIONI:oNOT EQUAL TOSUBSET OF OR EQUAL TO  [n] (MINUS SIGN 1)|I|+1?(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.

Název v anglickém jazyce

Simplifying inclusion-exclusion formulas

Popis výsledku anglicky

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 ? on S, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that ? (F 1 UNION F 2 UNION...UNION F n) = N-ARY SUMMATIONI:oNOT EQUAL TOSUBSET OF OR EQUAL TO  [n] (MINUS SIGN 1)|I|+1?(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.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Kreslení grafů a jejich geometrické reprezentace</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

The Seventh European Conference on Combinatorics, Graph Theory and Applications; EuroComb 2013

ISBN

978-88-7642-474-8

ISSN

—

e-ISSN

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Počet stran výsledku

7

Strana od-do

559-565

Název nakladatele

Scuola Normale Superiore

Místo vydání

Pisa

Místo konání akce

Pisa

Datum konání akce

9. 9. 2013

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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