Sebastien Collette

A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More…

It is shown how to enhance any data structure in the pointer model to make it confluently persistent, with efficient query and update times and limited space overhead. Updates are performed in $O(\log n)$ amortized time, and following a…

In this paper, we analyze the time complexity of finding regular polygons in a set of n points. We combine two different approaches to find regular polygons, depending on their number of edges. Our result depends on the parameter alpha,…

We consider the theoretical model of Crystalline robots, which have been introduced and prototyped by the robotics community. These robots consist of independently manipulable unit-square atoms that can extend/contract arms on each side and…

A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to…

Let C be a compact and convex set in the plane that contains the origin in its interior, and let S be a finite set of points in the plane. The Delaunay graph DG_C(S) of S is defined to be the dual of the Voronoi diagram of S with respect to…

We propose a variant of Cauchy's Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its endpoints increases. The main focus of this work is a…