We present an algorithm which computes the overlay Hb r+ rIg of two Simply connected planar subdivisions~b and Hg; we assume that~b (resp.~) and all its components are colored in blue (resp. green). The algorithm runs in O(n + k) time and space, where n denotes the total nuruber of edges of~b and IIg and k the number of intersections between blue and green edges.
The join of two or even more multuiimensionalfiles has been discussed in detail for the binary equijoin. We propose an algorithm for the eficient evaluation of generaljoins on gruifiles. Since the implementation of the directory and the scales of the gridfile has been left open in the original grid file concept, we first discuss these issues und present the new BR2-directory representation. The grdfile can also be used to store geometric objects by trunsforming these objects into higher-dimensional points. Our algorithm also handles geometric joins on such data sets. We have developed a cost model to analyze the performance of our join algorithm. We present results concerning the binary equijoin and a special geometric join in this paper.
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