Multilevel Polynomial Partitions and Simplified Range Searching
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10315903" target="_blank" >RIV/00216208:11320/15:10315903 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00454-015-9701-2" target="_blank" >http://dx.doi.org/10.1007/s00454-015-9701-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00454-015-9701-2" target="_blank" >10.1007/s00454-015-9701-2</a>
Alternative languages
Result language
angličtina
Original language name
Multilevel Polynomial Partitions and Simplified Range Searching
Original language description
The polynomial partitioning method of Guth and Katz (arXiv:1011.4105) has numerous applications in discrete and computational geometry. It partitions a given n-point set using the zero set Z(f) of a suitable d-variate polynomial f. Applications of this result are often complicated by the problem, "What should be done with the points of P lying within Z(f)?" A natural approach is to partition these points with another polynomial and continue further in a similar manner. So far this has been pursued withlimited success-several authors managed to construct and apply a second partitioning polynomial, but further progress has been prevented by technical obstacles. We provide a polynomial partitioning method with up to d polynomials in dimension d, which allows for a complete decomposition of the given point set. We apply it to obtain a new algorithm for the semialgebraic range searching problem. Our algorithm has running time bounds similar to a recent algorithm by Agarwal et al. (SIAM J C
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
IN - Informatics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</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
Discrete and Computational Geometry
ISSN
0179-5376
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
22-41
UT code for WoS article
000355340300003
EID of the result in the Scopus database
2-s2.0-84930576142