Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00555605" target="_blank" >RIV/67985807:_____/21:00555605 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3233/FI-2021-2097" target="_blank" >http://dx.doi.org/10.3233/FI-2021-2097</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3233/FI-2021-2097" target="_blank" >10.3233/FI-2021-2097</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model

Popis výsledku v původním jazyce

The k-center problem is to choose a subset of size k from a set of n points such that the maximum distance from each point to its nearest center is minimized. Let Q = {Q1,... , Qn} be a set of polygons or segments in the region-based uncertainty model, in which each Qi is an uncertain point, where the exact locations of the points in Qi are unknown. The geometric objects such as segments and polygons can be models of a point set. We define the uncertain version of the k-center problem as a generalization in which the objective is to find k points from Q to cover the remaining regions of Q with minimum or maximum radius of the cluster to cover at least one or all exact instances of each Qi, respectively. We modify the region-based model to allow multiple points to be chosen from a region, and call the resulting model the aggregated uncertainty model. All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822 for the approximation factor. We give approximation algorithms for uncertain k-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice.

Název v anglickém jazyce

Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model

Popis výsledku anglicky

The k-center problem is to choose a subset of size k from a set of n points such that the maximum distance from each point to its nearest center is minimized. Let Q = {Q1,... , Qn} be a set of polygons or segments in the region-based uncertainty model, in which each Qi is an uncertain point, where the exact locations of the points in Qi are unknown. The geometric objects such as segments and polygons can be models of a point set. We define the uncertain version of the k-center problem as a generalization in which the objective is to find k points from Q to cover the remaining regions of Q with minimum or maximum radius of the cluster to cover at least one or all exact instances of each Qi, respectively. We modify the region-based model to allow multiple points to be chosen from a region, and call the resulting model the aggregated uncertainty model. All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822 for the approximation factor. We give approximation algorithms for uncertain k-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GJ19-06792Y" target="_blank" >GJ19-06792Y: Strukturální vlastnosti viditelnosti terénů a Voroného diagramů nejvzdálenější barvy</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Fundamenta Informaticae

ISSN

0169-2968

e-ISSN

1875-8681

Svazek periodika

184

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

27

Strana od-do

205-231

Kód UT WoS článku

000768541900002

EID výsledku v databázi Scopus

2-s2.0-85125177114