An index structure for spatial joins in linear constraint databases

Constraint databases integrate database technology with constraint solving to deal with new applications such as spatial or geographical applications and those requiring arithmetic computations. Although the conceptual framework is elegant, issues related to efficient query evaluation and optimization techniques have not been sufficiently addressed. We study efficient evaluation of spatial join in linear constraint databases in terms of the I/O complexity. We develop an extension of the classical B⁺-trees, called interval B⁺ -trees, and show that they can be used to efficiently evaluate the spatial join of relations with dense-order and linear constraints. Specifically, we develop a general algorithm for joining two sets of rectangles using interval B⁺-trees. We show that the algorithm has the worst case I/O complexity of O(bNlog_b(N/b)+k), where N is the number of input rectangles and k the number of intersections. We show that the algorithm can be used in performing joins of relations with linear constraints. For relations with dense-order constraints where the spatial objects are not strictly rectangles, we extend the algorithm so that it can process the natural join of two N-tuple relations within O(bNlog_b(N/b)+k) I/Os, where k is the number of intersections. It remains open if one can achieve the same upper bound in the linear case