A randomized algorithm for finding a maximum clique in the visibility graph of a simple polygon

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43925391" target="_blank" >RIV/49777513:23520/15:43925391 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2516" target="_blank" >http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/2516</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A randomized algorithm for finding a maximum clique in the visibility graph of a simple polygon

Popis výsledku v původním jazyce

We present a randomized algorithm to compute a clique of maximum size in the visibility graph $G$ of the vertices of a simple polygon $P$. The input of the problem consists of the visibility graph $G$, a Hamiltonian cycle describing the boundary of $P$,and a parameter $delta in (0,1)$ controlling the probability of error of the algorithm. The algorithm does not require the coordinates of the vertices of $P$. With probability at least $1-delta$ the algorithm runs in begin{math} Oleft( frac{|E(G)|^2}{omega(G)}log (1/delta) right) end{math} time and returns a maximum clique, where $omega(G)$ is the number of vertices in a maximum clique in $G$. A deterministic variant of the algorithm takes $O(|E(G)|^2)$ time and always outputs a maximum sizeclique. This compares well to the best previous algorithm by Ghosh textit{et al.}~(2007) for the problem, which is deterministic and runs in $O(|V(G)|^2 , |E(G)|)$ time.

Název v anglickém jazyce

A randomized algorithm for finding a maximum clique in the visibility graph of a simple polygon

Popis výsledku anglicky

We present a randomized algorithm to compute a clique of maximum size in the visibility graph $G$ of the vertices of a simple polygon $P$. The input of the problem consists of the visibility graph $G$, a Hamiltonian cycle describing the boundary of $P$,and a parameter $delta in (0,1)$ controlling the probability of error of the algorithm. The algorithm does not require the coordinates of the vertices of $P$. With probability at least $1-delta$ the algorithm runs in begin{math} Oleft( frac{|E(G)|^2}{omega(G)}log (1/delta) right) end{math} time and returns a maximum clique, where $omega(G)$ is the number of vertices in a maximum clique in $G$. A deterministic variant of the algorithm takes $O(|E(G)|^2)$ time and always outputs a maximum sizeclique. This compares well to the best previous algorithm by Ghosh textit{et al.}~(2007) for the problem, which is deterministic and runs in $O(|V(G)|^2 , |E(G)|)$ time.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: Nová excelence lidských zdrojů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE

ISSN

1365-8050

e-ISSN

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Svazek periodika

17

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

000352198400001

EID výsledku v databázi Scopus

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