We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R 2 ) or the skip octree (for point data in R d , with constant d > 2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for

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... her dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location, approximate range, and approximate nearest neighbor queries. are contained in a given query region. We are interested in this paper in data structures for multidimensional point sets that are dynamic, in that they allow for fast point insertion and deletion, as well as efficient, in that they use linear space and allow for fast query times.