Affiliation:
1. Hong Kong University of Science and Technology, Hong Kong, China
2. King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Abstract
We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with
n
vertices, among which
r
are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in
O
(
n
(log
n
)log
r
) time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected
O
(
n
sqrt
h
+ 1 log
2
n
) time for a polygon with
h
holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a nondegenerate polygon in
O
(
n
(log
n
)log
r
+
r
4/3 + ε
) time for any ε > 0. On degenerate input, our time bound increases to
O
(
n
(log
n
)log
r
+
r
17/11 + ε
).
Funder
Research Grants Council, Hong Kong, China
KAUST
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Cited by
8 articles.
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