Efficient approximation algorithms for clustering point-sets
In this paper, we consider the problem of clustering a set of n finite point-sets in d-dimensional Euclidean space. Different from the traditional clustering problem (called points clustering problem where the to-be-clustered objects are points), the point-sets clustering problem requires that all p...
Saved in:
| Published in: | Computational geometry : theory and applications Vol. 43; no. 1; pp. 59 - 66 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
2010
|
| Subjects: | |
| ISSN: | 0925-7721 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we consider the problem of clustering a set of
n finite point-sets in
d-dimensional Euclidean space. Different from the traditional clustering problem (called points clustering problem where the to-be-clustered objects are points), the point-sets clustering problem requires that all points in a single point-set be clustered into the same cluster. This requirement disturbs the metric property of the underlying distance function among point-sets and complicates the clustering problem dramatically. In this paper, we use a number of interesting observations and techniques to overcome this difficulty. For the
k-center clustering problem on point-sets, we give an
O
(
m
+
n
log
k
)
-time 3-approximation algorithm and an
O
(
k
m
)
-time
(
1
+
3
)
-approximation algorithm, where
m is the total number of input points and
k is the number of clusters. When
k is a small constant, the performance ratio of our algorithm reduces to
(
2
+
ϵ
)
for any
ϵ
>
0
. For the
k-median problem on point-sets, we present a polynomial time
(
3
+
ϵ
)
-approximation algorithm. Our approaches are rather general and can be easily implemented for practical purpose. |
|---|---|
| ISSN: | 0925-7721 |
| DOI: | 10.1016/j.comgeo.2007.12.002 |