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The notion of staircase separator, introduced in [2], greatly facilitates the design of divide-and-conquer algorithms for problems on rectangles. We generalize the concept of staircase separator to k-perfect staircase separator, namely a set of staircase separators which partitions a set S of n axis-parallel, rectangles into k subsets of (almost) equal size. We derive an optimal O(logn) time parallel...
Spatial Data Management and Spatial Data Processing often requires technology of many different computer science disciplines like Data Management, Computational Geometry, Statistics, and Data Visualisation. Todays GIS try to integrate this technology into one single, large, software package. We propose a new flexible solution for keeping the specialised software packages independent and autonomous...
We describe a unified framework for representing and manipulating binary topological relationships between complex regions, which are arbitrary compositions of homogeneous 2-dimensional surfaces, possibly with holes. Previously, compositions of regions and regions with holes were treated separately and in a restrictive scenario, where it is required that the composing regions should be disconnected...
In this paper we prove the existence of binary space partitions (BSPs) with linear size for sets of axis-parallel boxes in three dimensional space under certain conditions that are often satisfied in practical situations. In particular, we give an O(n log n) time algorithm to construct a BSP tree with linear size for a set S of axis-parallel boxes where the ratio between the lengths of the longest...
Graphical representations to illustrate basic concepts of spatial access structures or to explain the behaviour of such data structures are widely used, not only in the relevant literature. Although computer-based tools to create such visualizations can be a valuable help for presentation, analysis or even for debugging of such access structures, to our knowledge no such tool is yet available. As...