TY - JOUR

T1 - Closest pair and the post office problem for stochastic points

AU - Kamousi, Pegah

AU - Chan, Timothy M.

AU - Suri, Subhash

N1 - Funding Information:
The work of the first and the third author was supported in part by National Science Foundation grants CCF-0514738 and CNS-1035917 . The work of the second author was supported by NSERC . A preliminary version of the paper has appeared in: Proc. 12th Algorithms and Data Structures Symposium (WADS), 2011, pp. 548–559.

PY - 2014

Y1 - 2014

N2 - Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point miâ̂̂M with an independent probability pi. 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? These basic computational geometry problems, whose complexity is quite well-understood in the deterministic setting, prove to be surprisingly hard in our stochastic setting. We obtain hardness results and approximation algorithms for stochastic problems of this kind.

AB - Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point miâ̂̂M with an independent probability pi. 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? These basic computational geometry problems, whose complexity is quite well-understood in the deterministic setting, prove to be surprisingly hard in our stochastic setting. We obtain hardness results and approximation algorithms for stochastic problems of this kind.

KW - Approximation algorithms

KW - Computational geometry

KW - Data structures

KW - Probabilistic optimization

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U2 - 10.1016/j.comgeo.2012.10.010

DO - 10.1016/j.comgeo.2012.10.010

M3 - Article

AN - SCOPUS:84887467448

VL - 47

SP - 214

EP - 223

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 2 PART A

ER -