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Published in:
2010 | OriginalPaper | Chapter
Approximate Shortest Homotopic Paths in Weighted Regions
Authors : Siu-Wing Cheng, Jiongxin Jin, Antoine Vigneron, Yajun Wang
Published in: Algorithms and Computation
Publisher: Springer Berlin Heidelberg
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Let
P
be a path between two points
s
and
t
in a polygonal subdivision
$\mathcal T$
with obstacles and weighted regions. Given a relative error tolerance
ε
∈ (0,1), we present the first algorithm to compute a path between
s
and
t
that can be deformed to
P
without passing over any obstacle and the path cost is within a factor 1 +
ε
of the optimum. The running time is
$O(\frac{h^3}{\varepsilon^2}kn\,\mathrm{polylog}(k,n,\frac{1}{\varepsilon}))$
, where
k
is the number of segments in
P
and
h
and
n
are the numbers of obstacles and vertices in
$\mathcal T$
, respectively. The constant in the running time of our algorithm depends on some geometric parameters and the ratio of the maximum region weight to the minimum region weight.