We introduce the exact coloured k-enclosing object problem: given a set P of n points in R, each of which has an associated colour in {1, . . . , t}, and a vector c = (c1, . . . , ct), where ci âˆˆ Zâ€¦ (More)

For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle &thetas; = 2Ï€/k, and connects each point to aâ€¦ (More)

For a polyhedron P in R, denote by |P | its combinatorial complexity, i.e., the number of faces of all dimensions of the polyhedra. In this paper, we revisit the classic problem of preprocessingâ€¦ (More)

The 3SUM problem asks if an input n-set of real numbers contains a triple whose sum is zero. We consider the 3POL problem, a natural generalization of 3SUM where we replace the sum function by aâ€¦ (More)

In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. Weâ€¦ (More)

We study the amortized number of combinatorial changes (edge insertions and removals) needed to update the graph structure of the Voronoi diagram VD(S) (and several variants thereof) of a set S of nâ€¦ (More)