Closest pair and the post office problem for stochastic points

Authors:
Pegah Kamousi;Timothy M. Chan;Subhash Suri
Affiliations:
Computer Science, UC Santa Barbara, CA;Computer Science, University of Waterloo, Ontario;Computer Science, UC Santa Barbara, CA
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

Given a (master) set M of n points in d-dimensional Euclidean space, consider drawing a random subset that includes each point mi ∈ M 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? We obtain hardness results and approximation algorithms for stochastic problems of this kind.