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
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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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
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e-ISSN
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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
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