Dynamic Euclidean minimum spanning trees and extrema of binary functions |
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Authors: | D. Eppstein |
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Affiliation: | (1) Department of Information and Computer Science, University of California, 92717 Irvine, CA, USA |
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Abstract: | We maintain the minimum spanning tree of a point set in the plane subject to point insertions and deletions, in amortized timeO(n 1/2 log2 n) per update operation. We reduce the problem to maintaining bichromatic closest pairs, which we solve in timeO(n e ) per update. Our algorithm uses a novel construction, theordered nearest neighbor path of a set of points. Our results generalize to higher dimensions, and to fully dynamic algorithms for maintaining minima of binary functions, including the diameter of a point set and the bichromatic farthest pair. This research was supported in part by NSF Grant CCR-9258355 |
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