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Discrete & Computational Geometry

, Volume 13, Issue 1, pp 111–122 | Cite as

Dynamic Euclidean minimum spanning trees and extrema of binary functions

  • D. Eppstein
Article

Abstract

We maintain the minimum spanning tree of a point set in the plane subject to point insertions and deletions, in amortized timeO(n1/2 log2n) 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.

Keywords

Minimum Span Tree Binary Function Dynamic Algorithm Double Wedge Amortize Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1995

Authors and Affiliations

  • D. Eppstein
    • 1
  1. 1.Department of Information and Computer ScienceUniversity of CaliforniaIrvineUSA

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