Efficient 3-D range searching in external memory

We present a new approach to designing data structures for the important problem of externalmemory range searching in two and three dimensions. We construct data structures for answering range queries in O ( (log log log~ N) logB N + K/B) 1/0 operations, where N is the number of points in the data structure, B is the 1/0 block size, and K is the number of points in the answer to the query. We base our data structures on the novel concept of B-approximate boundaries, which are manifolds that partition space into regions based on the output size of queries at points within the space. Our data structures answer a longstanding open problem by providing three dimensional results comparable to those provided by [8, 10] for the two dimensional case, though completely new techniques are used. Ours is the first 3-D range search data structure that simultaneously achieves both a base-B logarithmic search overhead (namely, (log log log~ N) logB N) and a fully blocked output component (namely, K/B). This gives us an *Supported in part by the U.S. Army Research Office under grant DAAH04–93–G–O076 and by the National Science Foundation under grant DMR–9217290. Portions of this work were conducted while visiting the University of Michigan. +Supported in part by the National Science Foundation under grant CCR–9522047, and by the U.S. Army Research Office under grant DAAH04-93-G-O076. Permission to make digitellhard copies of all or pan of thk material for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication and its date appear, and notice ia given that copyright ia by permission of the ACM, Inc. To copy olherwiae, to reoublish. to ooat on servers or to radktribute to tists, requiraa specific perrsr fee. STOC’96, Philadelphia PA, USA 01996 ACM ()-89791-785-5/96/05. .$3.50 Jeffrey Scott Vittert Duke University