For applying the sweep-line method, a state space reduction technique, it is necessary to provide an automatic calculation of a progress measure. In [1], such a calculation has been proposed for Petri nets. The approach presented there may lead to suboptimal results, therefore the author suggested possible optimizations. In this paper, we check whether the proposed optimization goals indeed lea...

We present data structures for maintaining the relative convex hull of a set of points (sites) in the presence of pairwise non-crossing line segments (barriers) that subdivide a bounding box into simply connected faces. Our data structures have O((n + m) log n) size for n sites and m barriers. They support O(m) barrier insertions and O(n) site deletions in O((m + n) polylog (mn)) total time, an...

The greedy triangulation of a nite planar point set is obtained by repeatedly inserting a shortest diagonal that doesn't intersect those already in the plane. We show that the problem of constructing the greedy triangulation of a nite set of points with integer coordinates in the plane is P-complete. This is the rst known geometric P-complete problem where the input is given as a set of points....

We introduce a framework for the construction, maintenance, and manipulation of arrangements of curves embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The framework applies to planes, cylinders, spheres, tori, and surfaces homeomorphic to them. We reduce the effort needed to generalize existing algorithms, such as the sweep line and zone traversal ...

We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation...