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

Result code in 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>
Result on the web
<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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Result language
angličtina
Original language name
A randomized algorithm for finding a maximum clique in the visibility graph of a simple polygon
Original language description
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.
Czech name
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Czech description
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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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Project
<a href="/en/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: New excellence in human resources</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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