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Erschienen in:
2008 | OriginalPaper | Buchkapitel
On the Stretch Factor of Convex Delaunay Graphs
verfasst von : Prosenjit Bose, Paz Carmi, Sébastien Collette, Michiel Smid
Erschienen in: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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Let
C
be a compact and convex set in the plane that contains the origin in its interior, and let
S
be a finite set of points in the plane. The Delaunay graph
$\mathord{\it DG}_C(S)$
of
S
is defined to be the dual of the Voronoi diagram of
S
with respect to the convex distance function defined by
C
. We prove that
$\mathord{\it DG}_C(S)$
is a
t
-spanner for
S
, for some constant
t
that depends only on the shape of the set
C
. Thus, for any two points
p
and
q
in
S
, the graph
$\mathord{\it DG}_C(S)$
contains a path between
p
and
q
whose Euclidean length is at most
t
times the Euclidean distance between
p
and
q
.