June 2011 Probabilistic results for a mobile service scenario
Jesper Møller, Man Lung Yiu
Author Affiliations +
Adv. in Appl. Probab. 43(2): 322-334 (June 2011).


We consider the following stochastic model for a mobile service scenario. Consider a stationary Poisson process in Rd, with its points radially ordered with respect to the origin (the anchor); if d = 2, the points may correspond to locations of, e.g. restaurants. A user, with a location different from the origin, asks for the location of the first Poisson point and keeps asking for the location of the next Poisson point until the first time that he/she can be completely certain that he/she knows which Poisson point is his/her nearest neighbour. This waiting time is the communication cost, while the inferred privacy region is a random set obtained by an adversary who only knows the anchor and the points received from the server, where the adversary `does the best' to infer the possible locations of the user. Probabilistic results related to the communication cost and the inferred privacy region are established for any dimension d ≥ 1. Furthermore, special results when d = 1 and particularly when d = 2 are derived.


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Jesper Møller. Man Lung Yiu. "Probabilistic results for a mobile service scenario." Adv. in Appl. Probab. 43 (2) 322 - 334, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1225.60083
MathSciNet: MR2848378

Primary: 60D05 , 60G55 , 62M30
Secondary: 68U20

Keywords: Communication cost , nearest-neighbour search , Poisson process , privacy region , radial simulation algorithm , Voronoi tessellation

Rights: Copyright © 2011 Applied Probability Trust


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Vol.43 • No. 2 • June 2011
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