We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable ...

We study the problem of computing the similarity between two piecewise-linear bivariate functions de ned over a common domain, where the surfaces they de ne in 3D|polyhedral terrains|can be transformed vertically by a ...

We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the arithmetic mean of the distances between all pairs of vertices. This parameter ...

The farthest-color Voronoi diagram (FCVD) is a farthestsite Voronoi structure defined on a family P of m point-clusters in the plane, where the total number of points is n. The FCVD finds applications in problems related ...

We study water flow computation on imprecise terrains. We consider two approaches to modeling flow on a terrain: one where water flows across the surface of a polyhedral terrain in the direction of steepest descent, and ...

Motivated by a technique in privacy protection, in which n points are randomly perturbed by at most a distance r, we study the following problem: Given n points and m circles in the plane, what is the maximum r such that ...

We study biplane graphs drawn on a finite point set in the plane in general position. This is the family of geometric graphs whose vertex set is and which can be decomposed into two plane graphs. We show that every ...

We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape C. Let S be a point set in the plane. ...

We study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(S), has vertex set S and edge pq provided ...