We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or pe...

We provide constant ratio approximation algorithms for two NP-hard problems, the rectangle stabbing problem and the rectilinear partitioning problem. In the rectangle stabbing problem, we are given a set of rectangles in two-dimensional space, with the objective of stabbing all rectangles with the minimum number of lines parallel to the x and y axes. We provide a 2-approximation algorithm, whil...

This paper presents a counterexample for the approximation algorithm proposed by Durocher and Mehrabi [1] for the general problem of finding a rectangular partition of a rectilinear polygon with minimum stabbing number.

This paper introduces the Dynamic Cascade Tree (DCT), a structure designed to index query regions on multi-dimensional data streams. The DCT is designed for a stream management system with a particular focus on Remotely-Sensed Imagery (RSI) data streams. For these streams, an important query operation is to efficiently restrict incoming geospatial data to specified regions of interest. As nearl...

Many graphics applications today have to cope with large amounts of data. A popular approach to reduce the amount of geometry to be rendered is to precompute visibility in order to render only objects that can be seen from the given viewpoint. This paper presents one technique to achieve this, potentially visible sets (PVS). These sets are used to avoid rendering hidden objects, especially geom...

Short-lasting headaches have been studied infrequently in children and it is not known if the main categories of primary headaches of this type in adults are applicable to children. We report our experience with a group of 20 children with a brief headache. Two patients had a secondary headache. One patient had a headache with some clinical characteristics of paroxysmal hemicrania. The remainin...

Let P be an orthogonal polygon with n vertices. A partition of P into rectangles is called conforming if it results from cutting P along a set of interior-disjoint line segments, each having both endpoints on the boundary of P . The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any orthogonal line segment inside P . In this paper, we consider...