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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Square and Rectangle Covering with Outliers
verfasst von : Hee-Kap Ahn, Sang Won Bae, Sang-Sub Kim, Matias Korman, Iris Reinbacher, Wanbin Son
Erschienen in: Frontiers in Algorithmics
Verlag: Springer Berlin Heidelberg
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For a set of
n
points in the plane, we consider the axis–aligned (
p
,
k
)
-Box Covering
problem: Find
p
axis-aligned, pairwise disjoint boxes that together contain exactly
n
−
k
points. Here, our boxes are either squares or rectangles, and we want to minimize the area of the largest box. For squares, we present algorithms that find the solution in
O
(
n
+
k
log
k
) time for
p
= 1, and in
O
(
n
log
n
+
k
p
log
p
k
) time for
p
= 2,3. For rectangles we have running times of
O
(
n
+
k
3
) for
p
= 1 and
O
(
n
log
n
+
k
2 +
p
log
p
− 1
k
) time for
p
= 2,3. In all cases, our algorithms use
O
(
n
) space.