This paper is concerned with a memory-efficient representation of reachability graphs. We describe a technique that enables us to represent each reachable marking in a number of bits close to the theoretical minimum needed for explicit state enumeration. The technique maps each state vector onto a number between zero and the number of reachable states and uses the sweep-line method to delete th...

A new generalized Voronoi diagram is defined on the surface of a river with unifonn flow; a point belongs to the territory of a site if and only if a boat starting from the site can reach the point faster than a boat starting from any other site. If the river runs slower than the boat, the Voronoi diagram can be obtained from the ordinary Voronoi diagram by a certain transformation, whereas if ...

We examine the space requirement for the classic linesegment intersection problem. Using so-called implicit data structures, we show how to make the standard sweep-line algorithm run in O((n+ k) log n) time with only O(log n) extra space, where n is the number of line segments and k is the number of intersections. If division is allowed and input can be destroyed, the algorithm can run in O((n ...

We give a tight analysis of an old and popular sweep-line heuristic for constructing a spanning tree of a set of n points in the plane. The algorithm sweeps a vertical line across the input points from left to right, and each point is connected by a straight line segment to the closest point left of (or on) the sweep-line. If W denotes the weight the Euclidean minimum spanning tree (EMST), the ...

We have extended Fortune’s sweep-line algorithm for the construction Voronoi diagrams in the plane to the surface of a sphere. Although the extension is straightforward, it requires interesting modifications. The main difference between the sweep line algorithms on plane and on the sphere is that that the beach line on the sphere is a closed curve. We have implemented this algorithm and tessell...

Voronoi diagrams are among the most important data structures in geometric modeling. Among many efficient algorithms for computing 2D Voronoi diagrams, Fortune’s sweepline algorithm (Fortune, 1986 [5]) is popular due to its elegance and simplicity. Dehne and Klein (1987) [8] extended sweepline to sweepcircle and suggested computing a type of transformed Voronoi diagram, which is parallel in nat...