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