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Simplifying Inclusion-Exclusion Formulas

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Simplifying Inclusion-Exclusion Formulas

  • Original language 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 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

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GEGIG%2F11%2FE023" target="_blank" >GEGIG/11/E023: Graph Drawings and Representations</a><br>

  • Continuities

    S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2015

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Combinatorics Probability and Computing

  • ISSN

    0963-5483

  • e-ISSN

  • Volume of the periodical

    24

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    19

  • Pages from-to

    438-456

  • UT code for WoS article

    000348383500004

  • EID of the result in the Scopus database

    2-s2.0-84922021557