Guarding Vertices versus Guarding Edges in a Simple Polygon
Abstract
Let $P$ be a simple polygon, $V$ its set of vertices. A minimal
vertex cover $C$ of $P$ is a minimal subset of $V$ which covers $V$.
The extended cover of $P$ given $C$ is the maximal subset of the
boundary of $P$ covered by $C$. Let $\epsilon P$ denotes the
extended cover of $P$ given $C$, and $\bar{\epsilon}P$ the complement
of $\epsilon P$ with respect to $\delta P$. Denote by $\mu$ the
cardinality of $\bar{\epsilon}P$. In this paper we establish lower and
upper bounds on $\mu$ as a function of $n$ the cardinality of the edge
set of $P$ and $k$ the cardinality of the covering set. In the
restricted case where $k = 2$ we prove the bounds to be tight.
Fichier principal
cccg92.pdf (166.02 Ko)
Télécharger le fichier
vignette (1).png (26.77 Ko)
Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)