Abstract not found

In this paper we investigate automated methods for externalizing internal memory data structures. We consider a class of balanced trees that we call weight-balanced partitioning trees (or wp-trees) for indexing a set of points in R d . Well-known examples of wp-trees include kd- trees, BBD-trees, pseudo-quad-trees, and BAR-trees. Given an efficient external wp-tree construction algorithm, we present a general framework for automatically obtaining a dynamic external data structure. Using this framework together with a new general construction (bulk loading) technique of independent interest, we obtain data structures with guaranteed good update performance in terms of I/O transfers. Our approach gives considerably improved construction and update I/O bounds for e.g. external kd-trees and BBD-trees.

Abstract. We show that a popular variant of the well known k-d tree data structure satisfies an important packing lemma. This variant is a binary spatial partitioning tree T defined on a set of n points in IR d, for fixed d ≥ 1, using the simple rule of splitting each node’s hyperrectangular region with a hyperplane that cuts the longest side. An interesting consequence of the packing lemma is that standard algorithms for performing approximate nearest-neighbor searching or range searchingqueriesvisitatmostO(log d−1 n)nodesofsuchatreeT in the worst case. Traditionally, many variants of k-d trees have been empirically shown to exhibit polylogarithmic performance, and under certain restrictions in the data distribution some theoretical expected case results have been proven. This result, however, is the first one proving a worst-case polylogarithmic time bound for approximate geometric queries using the simple k-d tree data structure. 1