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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Exact Algorithms for 2-Clustering with Size Constraints in the Euclidean Plane
verfasst von : Alberto Bertoni, Massimiliano Goldwurm, Jianyi Lin
Erschienen in: SOFSEM 2015: Theory and Practice of Computer Science
Verlag: Springer Berlin Heidelberg
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We study the problem of determining an optimal bipartition {
A
,
B
} of a set
X
of
n
points in ℝ
2
that minimizes the sum of the sample variances of
A
and
B
, under the size constraints |
A
| =
k
and |
B
| =
n
−
k
. We present two algorithms for such a problem. The first one computes the solution in
$O(n\sqrt[3]{k}\log^2 n)$
time by using known results on convex-hulls and
k
-sets. The second algorithm, for an input
X
⊂ ℝ
2
of size
n
, solves the problem for all
$k=1,2,\ldots,\lfloor n/2\rfloor$
and works in
O
(
n
2
log
n
) time.