Abstract
We present an external memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set P in ℝd in O(sort(N)) I/Os using O(N/B) blocks of external memory, where N is the number of points in P, and sort(N) denotes the I/O complexity of sorting N items. (Throughout this paper we assume that the dimension d is fixed). We also show how to dynamically maintain the WSPD in O(log BN) I/O’s per insert or delete operation using O(N/B) blocks of external memory. As applications of the WSPD, we show how to compute a linear size t-spanner for P within the same I/O and space bounds and how to solve the K-nearest neighbor and K-closest pair problems in O(sort(KN)) and O(sort(N + K)) I/Os using O(KN/B) and O((N + K)/B) blocks of external memory, respectively. Using the dynamic WSPD, we show how to dynamically maintain the closest pair of P in O(log BN) I/O’s per insert or delete operation using O(N/B) blocks of external memory.
Research supported by NSERC, NCE GEOIDE, and by DFG-SFB376.
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Govindarajan, S., Lukovszki, T., Maheshwari, A., Zeh, N. (2000). I/O-Efficient Well-Separated Pair Decomposition and Its Applications. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_21
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DOI: https://doi.org/10.1007/3-540-45253-2_21
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