IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
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For a collection of sets in Rd we consider the task of finding all sets in the collection that cover or contain a given point. The algorithms introduced in this paper are based on quadtrees and their generalizations to Rd. The advantages of our new splitting algorithm to find the covering sets of a point over the basic algorithm are detailed by means of hit rates and the expected depth traversed in the quadtree search, numerically and theoretically. This solves a difficult problem faced by mesh-free discretizations of partial differential equations.