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COMPGEOM
2009
ACM
15 years 9 months 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
15 years 11 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»
15 years 11 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»
15 years 4 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»
15 years 4 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