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» Three-Clustering of Points in the Plane
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SODA
1997
ACM
144views Algorithms» more  SODA 1997»
15 years 7 months ago
Methods for Achieving Fast Query Times in Point Location Data Structures
Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can e ciently determine for a given query point p the...
Michael T. Goodrich, Mark W. Orletsky, Kumar Ramai...
SMC
2007
IEEE
110views Control Systems» more  SMC 2007»
16 years 13 days ago
A validity index based on cluster symmetry
— An important consideration in clustering is the determination of the correct number of clusters and the appropriate partitioning of a given data set. In this paper, a newly dev...
Sriparna Saha, Sanghamitra Bandyopadhyay
ICALP
2004
Springer
15 years 11 months ago
Sublinear-Time Approximation for Clustering Via Random Sampling
Abstract. In this paper we present a novel analysis of a random sampling approach for three clustering problems in metric spaces: k-median, min-sum kclustering, and balanced k-medi...
Artur Czumaj, Christian Sohler
COMPGEOM
2009
ACM
16 years 21 days ago
On the topology of planar algebraic curves
We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of...
Jinsan Cheng, Sylvain Lazard, Luis Mariano Pe&ntil...
COMPGEOM
2007
ACM
15 years 10 months ago
An optimal generalization of the centerpoint theorem, and its extensions
We prove an optimal generalization of the centerpoint theorem: given a set P of n points in the plane, there exist two points (not necessarily among input points) that hit all con...
Saurabh Ray, Nabil H. Mustafa