Simplifying Inclusion-Exclusion Formulas

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10312208" target="_blank" >RIV/00216208:11320/15:10312208 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1017/S096354831400042X" target="_blank" >http://dx.doi.org/10.1017/S096354831400042X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/S096354831400042X" target="_blank" >10.1017/S096354831400042X</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 mu on S, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that mu(F-1 boolean OR F-2boolean OR . . . boolean OR F-n) = Sigma(I:phi not equal I subset of[n]) (-1)(|I|+1)mu(boolean AND F-i is an element of I(i)), that is, the measure of the union is expressed using measures of various intersections. The number of terms in this formula isexponential 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 setswith m non-empty 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. For every epsilon > 0 we also co

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 mu on S, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that mu(F-1 boolean OR F-2boolean OR . . . boolean OR F-n) = Sigma(I:phi not equal I subset of[n]) (-1)(|I|+1)mu(boolean AND F-i is an element of I(i)), that is, the measure of the union is expressed using measures of various intersections. The number of terms in this formula isexponential 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 setswith m non-empty 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. For every epsilon > 0 we also co

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

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<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Combinatorics Probability and Computing

ISSN

0963-5483

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

438-456

Kód UT WoS článku

000348383500004

EID výsledku v databázi Scopus

2-s2.0-84922021557