I/O-Efficient Well-Separated Pair Decomposition and Applications

Authors:
Sathish Govindarajan;Tamas Lukovszki;Anil Maheshwari;Norbert Zeh
Affiliations:
Department of Computer Science, Duke University, Durham, NC 27708-0129, USA;Heinz-Nixdorf-Institut and Department of Computer Science, University of Paderborn, Germany;School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada;Faculty of Computer Science, Dalhousie University, 6050 University Avenue, Halifax, Nova Scotia, B3H 1W5, Canada
Venue:
Algorithmica
Year:
2006

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Abstract

We present an external-memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set S in ℝd in O(sort(N)) I/Os, where N is the number of points in S and sort(N) denotes the I/O-complexity of sorting N items. (Throughout this paper we assume that the dimension d is fixed.) As applications of the WSPD, we show how to compute a linear-size t-spanner for S within the same I/O-bound and how to solve the K-nearest-neighbour and K-closest-pair problems in O(sort(KN)) and O(sort(N+K)) I/Os, respectively.