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Abstract:

The traditional spatial join evaluation strategy is to perform a join of "minimum bounding rectangles " (MBR) of the spatial objects and the join of the objects using the join results of MBR's. In this paper, we develop efficient algorithms for evaluating joins of "trapezoids " without using MBR's. When there are no intersecting non-horizontal boundaries in the same set, a spatial join of two N trapezoids sets can be done in O(N log b N+k) I/Os, and for the general case with no assumptions, a join can be done in O((N+l+k) log b N) I/Os, where b is the page size, k the number of trapezoid intersections, and l the number of non-horizontal boundary intersections within the same set. The new algorithms can be used to evaluate spatial joins for polygons. One possibility is to decompose polygons into trapezoids and apply a trapezoid join algorithm. In particular, this approach is efficient for "I/O bounded polygons " (each of which can be retrieved in a constant number of I/Os). We show that a spatial join of two sets of I/O bounded polygons, has the same complexity as a join of trapezoids. Another possibility is to approximate objects by I/O bounded polygons (e.g., 5-corner convex polygons) which are finer than rectangles and use the new algorithms as a filter. 1.

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