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COMPGEOM
2009
ACM
14 years 10 days ago
k-means requires exponentially many iterations even in the plane
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice....
Andrea Vattani
COMPGEOM
2009
ACM
14 years 2 months ago
Epsilon nets and union complexity
We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest su...
Kasturi R. Varadarajan
WALCOM
2010
IEEE
206views Algorithms» more  WALCOM 2010»
14 years 2 months ago
Crossings between Curves with Many Tangencies
Let A and B be two families of two-way infinite x-monotone curves, no three of which pass through the same point. Assume that every curve in A lies above every curve in B and that...
Jacob Fox, Fabrizio Frati, János Pach, Rom ...
COMBINATORICS
1999
139views more  COMBINATORICS 1999»
13 years 7 months ago
A Closer Look at Lattice Points in Rational Simplices
Abstract. We generalize Ehrhart's idea ([Eh]) of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n + 1...
Matthias Beck
SIAMCOMP
1998
92views more  SIAMCOMP 1998»
13 years 7 months ago
Surface Approximation and Geometric Partitions
Motivated by applications in computer graphics, visualization, and scienti c computation, we study the computational complexity of the following problem: Given a set S of n points...
Pankaj K. Agarwal, Subhash Suri