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Dynamic Euclidean minimum spanning trees and extrema of binary functions
1995
Discrete & Computational Geometry
We maintain the minimum spanning tree of a point set in the plane subject to point insertions and deletions, in amortized time O(n ~/2 log 2 n) per update operation. We reduce the problem to maintaining bichromatic closest pairs, which we solve in time O(n9 per update. Our algorithm uses a novel construction, the ordered 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
doi:10.1007/bf02574030
fatcat:4spdvj3vjrhobjgqrqtjwqss4q