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Closest Pair and the Post Office Problem for Stochastic Points

  • Pegah Kamousi
  • Timothy M. Chan
  • Subhash Suri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

Abstract

Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point m i  ∈ M with an independent probability p i . How difficult is it to compute elementary statistics about the closest pair of points in such a subset? For instance, what is the probability that the distance between the closest pair of points in the random subset is no more than ℓ, for a given value ℓ? Or, can we preprocess the master set M such that given a query point q, we can efficiently estimate the expected distance from q to its nearest neighbor in the random subset? We obtain hardness results and approximation algorithms for stochastic problems of this kind.

Keywords

Vertex Cover Query Point Random Subset Blue Point Close Pair 
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 Berlin Heidelberg 2011

Authors and Affiliations

  • Pegah Kamousi
    • 1
  • Timothy M. Chan
    • 2
  • Subhash Suri
    • 1
  1. 1.Computer ScienceUC Santa BarbaraUSA
  2. 2.Computer ScienceUniversity of WaterlooCanada

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