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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Tight Bound for Farthest-Color Voronoi Diagrams of Line Segments
verfasst von : Sang Won Bae
Erschienen in: WALCOM: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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We establish a tight bound on the worst-case combinatorial complexity of the farthest-color Voronoi diagram of line segments in the plane. More precisely, given
k
sets of total
n
line segments, the combinatorial complexity of the farthest-color Voronoi diagram is shown to be Θ(
kn
+
h
) in the worst case, under any
L
p
metric with 1 ≤
p
≤ ∞, where
h
is the number of crossings between the
n
line segments. We also show that the diagram can be computed in optimal
O
((
kn
+
h
)log
n
) time under the
L
1
or
L
∞
metric, or in
O
((
kn
+
h
) (
α
(
k
) log
k
+ log
n
)) time under the
L
p
metric for any 1 <
p
< ∞, where
α
(·) denotes the inverse Ackermann function.