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.
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This research was supported in part by NSF Grant CCR-9258355
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Eppstein, D. Dynamic Euclidean minimum spanning trees and extrema of binary functions. Discrete Comput Geom 13, 111–122 (1995). https://doi.org/10.1007/BF02574030
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DOI: https://doi.org/10.1007/BF02574030