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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%2F13%3A10190922" target="_blank" >RIV/00216208:11320/13:10190922 - isvavai.cz</a>

  • Result on the web

    <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>

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 ? 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.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • 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

Others

  • Publication year

    2013

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

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

  • ISBN

    978-88-7642-474-8

  • ISSN

  • e-ISSN

  • Number of pages

    7

  • Pages from-to

    559-565

  • Publisher name

    Scuola Normale Superiore

  • Place of publication

    Pisa

  • Event location

    Pisa

  • Event date

    Sep 9, 2013

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article