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.
https://hal.inria.fr/hal-01117277
Contributor : Olivier Devillers
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Submitted on : Thursday, February 19, 2015 - 11:13:03 AM
Last modification on : Saturday, January 27, 2018 - 1:31:25 AM
Long-term archiving on: Thursday, May 28, 2015 - 4:02:32 PM
Olivier Devillers, Naji Mouawad. Guarding Vertices versus Guarding Edges in a Simple Polygon. 4th Canadian Conference on Computational Geometry, 1992, St. John's, Canada. pp.99-102. ⟨hal-01117277⟩
