  We study the online problem of assigning a moving point to a base-station
region that contains it. For instance, the moving object could represent a
cellular phone and the base station could represent the coverage zones of cell
towers. Our goal is to minimize the number of handovers that occur when the
point moves outside its assigned region and must be assigned to a new region.
We study this problem in terms of competitive analysis and we measure the
competitive ratio of our algorithms as a function of the ply of the system of
regions, that is, the maximum number of regions that cover any single point. In
the offline version of this problem, when object motions are known in advance,
a simple greedy strategy suffices to determine an optimal assignment of objects
to base stations, with as few handovers as possible. For the online version of
this problem for moving points in one dimension, we present a deterministic
algorithm that achieves a competitive ratio of O(log ply) with respect to the
optimal algorithm, and we show that no better ratio is possible. For two or
more dimensions, we present a randomized online algorithm that achieves a
competitive ratio of O(log ply) with respect to the optimal algorithm, and a
deterministic algorithm that achieves a competitive ratio of O(ply); again, we
show that no better ratio is possible.
