@COMMENT {Autogenerated file by bib2html.pl version 0.94}
@Article{kt-artgal-2008,
author = {Menelaos I. Karavelas and Csaba D. T\'oth and Elias
P. Tsigaridas},
title = {Guarding curvilinear art galleries with vertex or
point guards},
journal = CGTA,
month = {Aug},
volume = 42,
number = {6-7},
pages = "522-535",
year = 2009,
abstract = " We study a variant of the classical art gallery
problem, where an art gallery is modeled by a
polygon with curvilinear sides. We focus on
\pconvex and \pconcave polygons, which are polygons
whose sides are convex and concave arcs,
respectively. It is shown that for monitoring a
\pconvex polygon with $n\geq 2$ vertices,
$\lfloor\frac{2n}{3}\rfloor$ vertex guards are
always sufficient and sometimes necessary. We also
present an algorithm for computing at most
$\lfloor\frac{2n}{3}\rfloor$ vertex guards in
$O(n\log n)$ time and $O(n)$ space. For the number
of point guards, can be be stationed at any point in
the polygon, our upper bound
$\lfloor\frac{2n}{3}\rfloor$ carries over and we
prove a lower bound of $\lceil \frac{n}{2}\rceil$.
For monitoring a \pconcave polygon with $n\geq 3$
vertices, $2n-4$ point guards are always sufficient
and sometimes necessary, whereas there are \pconcave
polygons where some points in the interior are
hidden from all vertices, hence they cannot be
monitored by vertex guards. We conclude with bounds
for some special types of curvilinear polygons.",
}