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....
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...
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...
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...
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...