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Randomized Data Structures for the Dynamic Closest-Pair Problem

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44509

Golin,  Mordecai J.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45250

Raman,  Rajeev
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45433

Schwarz,  Christian
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45509

Smid,  Michiel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-93-102.pdf
(Any fulltext), 349KB

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Citation

Golin, M. J., Raman, R., Schwarz, C., & Smid, M.(1993). Randomized Data Structures for the Dynamic Closest-Pair Problem (MPI-I-93-102). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B3F0-3
Abstract
We describe a new randomized data structure, the {\em sparse partition}, for solving the dynamic closest-pair problem. Using this data structure the closest pair of a set of $n$ points in $k$-dimensional space, for any fixed $k$, can be found in constant time. If the points are chosen from a finite universe, and if the floor function is available at unit-cost, then the data structure supports insertions into and deletions from the set in expected $O(\log n)$ time and requires expected $O(n)$ space. Here, it is assumed that the updates are chosen by an adversary who does not know the random choices made by the data structure. The data structure can be modified to run in $O(\log^2 n)$ expected time per update in the algebraic decision tree model of computation. Even this version is more efficient than the currently best known deterministic algorithms for solving the problem for $k>1$.