Multilevel Polynomial Partitions and Simplified Range Searching

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Multilevel Polynomial Partitions and Simplified Range Searching

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Multilevel Polynomial Partitions and Simplified Range Searching

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

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

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Discrete and Computational Geometry

ISSN

0179-5376

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

22-41

Kód UT WoS článku

000355340300003

EID výsledku v databázi Scopus

2-s2.0-84930576142