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We describe a uniied 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… (More)

We are given a set of n d-dimensional (possibly intersecting) isothetic hyperrectangles. The topic of this paper is the separation of these rectangles by means of a cutting isothetic hyperplane. Thereby we assume that a rectangle which is intersected by the cutting plane is cut into two non-overlapping hyperrectangles. We investigate the behavior of several… (More)

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, disjoint rectangles into k subsets of (almost)… (More)

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