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)


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.


Vertex Cover Query Point Random Subset Blue Point Close Pair 
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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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