An Onlognloglogn algorithm for the on-line closest pair problem

Authors:
Christian Schwarz;Michiel Smid
Affiliations:
-;-
Venue:
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Year:
1992

Citing 3
Cited 2

Optimal point location in a monotone subdivision

SIAM Journal on Computing
Rectangular Point Location and the Dynamic Closest Pair Problem

ISA '91 Proceedings of the 2nd International Symposium on Algorithms
Divide-and-conquer in multidimensional space

STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing

An optimal algorithm for the on-line closest-pair problem

SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An optimal algorithm for closest pair maintenance (extended abstract)

Proceedings of the eleventh annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let V be a set of n points in k-dimensional space. It is shown how the closest pair in V can be maintained under insertions in O(log n log log n) amortized time, using O(n) amortized time, using O(n) space. Distances are measured in the Lt-metric, where 1 ≤ ∞ . This gives an O(n log n log log n0 time on-line algorithm or computing the closest pair. The algorithm is based on Bentley's logarithmic method for decomposable searching problems. It uses a non-trivial extension of fractional cascading to k-dimensional space.