NDLI: Kinetic 2-centers in the black-box model

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Kinetic 2-centers in the black-box model

Content Provider	ACM Digital Library
Author	de Berg, Mark Speckmann, Bettina Roeloffzen, Marcel
Abstract	We study two versions of the 2-center problem for moving points in the plane. Given a set P of n points, the Euclidean 2-center problem asks for two congruent disks of minimum size that together cover P; the rectilinear 2-center problem correspondingly asks for two congruent axis-aligned squares of minimum size that together cover P. Our methods work in the black-box KDS model, where we receive the locations of the points at regular time steps and we know an upper bound d_{max} on the maximum displacement of any point within one time step. We show how to maintain the rectilinear 2-center in amortized sub-linear time per time step, under certain assumptions on the distribution of the point set P. For the Euclidean 2-center we give a similar result: we can maintain in amortized sub-linear time (again under certain assumptions on the distribution) a (1+ε)-approximation of the optimal 2-center. In many cases---namely when the distance between the centers of the disks is relatively large or relatively small---the solution we maintain is actually optimal. We also present results for the case where the maximum speed of the centers is bounded. We describe a simple scheme to maintain a 2-approximation of the rectilinear 2-center, and we provide a scheme which gives a better approximation factor depending on several parameters of the point set and the maximum allowed displacement of the centers. The latter result can be used to obtain a 2.29-approximation for the Euclidean 2-center; this is an improvement over the previously best known bound of 8/π approx 2.55. These algorithms run in amortized sub-linear time per time step, as before under certain assumptions on the distribution.
Starting Page	145
Ending Page	154
Page Count	10
File Format	PDF
ISBN	9781450320313
DOI	10.1145/2462356.2462393
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Mobile facility location Kinetic data structures Black-box model 2-center problem
Content Type	Text
Resource Type	Article

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