Affiliation:
1. Univ. of Waterloo, Waterloo, Ont., Canada
Abstract
We give a data structure that allows arbitrary insertions and deletions on a planar point set
P
and supports basic queries on the convex hull of
P
, such as membership and tangent-finding. Updates take
O
(log
1+ε
n
) amori tzed time and queries take
O
(log
n
time each, where
n
is the maximum size of
P
and ε is any fixed positive constant. For some advanced queries such as bridge-finding, both our bounds increase to
O
(log
3/2
n
). The only previous fully dynamic solution was by Overmars and van Leeuwen from 1981 and required
O
(log
2
n
) time per update and
O
(log
n
) time per query.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
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