We present a new line sweep algorithm, HeapSweep, for reporting bichromatic (`purple') intersections between a red and a blue family of line segments. If the union of the segments in each family is connected as a point set, HeapSweep reports all k purple intersections in time O((n + k)(n) log 3 n), where n is the total number of input segments and (n) is the familiar inverse Ackermann function....

This paper presents a new s cumulative constraint which generalizes the original cumulative constraint in different ways. The two most important aspects consist in permitting multiple cumulative resources as well as negative heights for the resource consumption of the tasks. This allows modeling in an easy way new scheduling and planning problems. The introduction of negative heights has forced...

We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, a simple plane-sweep algorithm is given that computes the Voronoi diagram for parallel halflines at logarithmic cost per face.

In this bachelor thesis we introduce the Squarability problem: When can a set of axisaligned rectangles be transformed into squares without changing combinatorial properties? This means, that we do not allow to change whether, how and in which order the rectangles respectively squares intersect. We use a sweep line algorithm to compute the combinatorial information from geometrically given rect...

In order to find all intersections among polygonal chains, this paper presents a procedure consisting of two phases: (1) splitting polygonal chains into a minimal number of monotone chains and (2) finding intersections among the monotone chains. For the first phase, we suggest an optimal algorithm splitting polygonal chains into a minimal number of monotone chains, with an Oðn þ r log rÞ time c...

A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating sweep-hull (sequentially created from the radially sorted set of 2D points, giving a non-overlapping triangulation), paired with a final triangle flipping step to give the Delaunay triangluation. In empirical tests the algorithm runs ...

We present a new polygon decomposition problem, the anchored area partition problem, which has applications to a multiple-robot terrain-covering problem. This problem concerns dividing a given polygon P into n polygonal pieces, each of a speciied area and each containing a certain point (site) on its boundary. We rst present the algorithm for the case when P is convex and contains no holes. The...

The plane sweep technique is one of the best known paradigms for the design of geometric algorithms [2]. Here an imaginary line sweeps over the plane while computing the property of interest at the moment the sweep line passes the required information needed to compute that property. There are also three-dimensional problems that are solved by space sweep, where a plane sweeps the space. This p...