2008 | OriginalPaper | Buchkapitel
An Approximate Algorithm for Solving the Watchman Route Problem
verfasst von : Fajie Li, Reinhard Klette
Erschienen in: Robot Vision
Verlag: Springer Berlin Heidelberg
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The watchman route problem (WRP) was first introduced in 1988 and is defined as follows: How to calculate a shortest route completely contained inside a simple polygon such that any point inside this polygon is visible from at least one point on the route? So far the best known result for the WRP is an
${\cal O}(n^3 \log n)$
runtime algorithm (with inherent numerical problems of its implementation). This paper gives an
$\kappa(\varepsilon)\times {\cal O}(kn)$
approximate algorithm for WRP by using a rubberband algorithm, where
n
is the number of vertices of the simple polygon,
k
the number of essential cuts,
ε
the chosen accuracy constant for the minimization of the calculated route, and
κ
(
ε
) equals the length of the initial route minus the length of the calculated route, divided by
ε
.