Belleville, P. and T.C. Shermer, Probing polygons minimally is hard, Computational Geometry: Theory and Applications 2 (1993) 255-265. Let r be a set of convex unimodal polygons in fixed position and orientation. We prove that the problem of determining whether k finger probes are sufficient to distinguish among the polygons in f is NP-complete for two types of finger probes. This implies that ...

In this paper we develop a discrete, T0 topology in which (1) closed sets play a more prominent role than open sets, (2) atoms comprising the space have discrete dimension, which (3) is used to define boundary elements, and (4) configurations within the topology can have connectivity (or separation) of different degrees. To justify this discrete, closure based topological approach we use it to ...

Arrangements of (pseudo-)circles have already been studied in connection with algorithms in computational geometry. Thereby information on the numbers v k of intersection points contained in k circles seems to be particularly interesting. On each circle, there is an induced arrangement of arcs. This is why we begin by studying arrangements of arcs, and we arrive at a complete characterization o...

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transf...

Let P be a simple polygon with n vertices. We say that P is k-guardable if it is possible to find a set of points Q consisting of interior points of edges of P such that every point of P is visible from at least k elements in Q and no edge of P has more than one element in Q. The following question was asked by A. Lubiw at the open problem session of the Fourth Canadian Conference in Computatio...

This paper is submitted for credit in the Algorithms for Polyhedra course at the University of Waterloo. We discuss a long-standing open problem in computational geometry and prove some partial results.

The paper presents a generic pruning technique that aggregates several constraints sharing some variables. The method is derived from an idea called sweep that is extensively used in computational geometry. A first benefit of this technique comes from the fact that it can be applied on several families of global constraints. A second main advantage is that it does not lead to any memory consump...

Gewali, L.P. and S. Ntafos, Covering grids and orthogonal polygons with periscope guards, Computational Geometry: Theory and Applications 2 (1993) 309-334. The problem of finding minimum guard covers is NP-hard for simple polygons and open for simple orthogonal polygons. Alternative definitions of visibility have been considered for orthogonal polygons. In this paper we try to determine the com...

Given a set P of n points in the plane and a multiset W of k weights with k ≤ n, we assign each weight in W to a distinct point in P to minimize the maximum weighted distance from the weighted center of P to any point in P . In this paper, we give two algorithms which take O(kn log n) time and O(kn log k + kn log n) time, respectively. For a constant k, the second algorithm takes only O(n log n...