Tracking Moving Objects with Few Handovers

TL;DR

This paper analyzes algorithms for assigning moving objects to base stations to minimize handovers, providing competitive ratios for online algorithms in various dimensions and establishing optimal bounds.

Contribution

It introduces online algorithms with proven competitive ratios for the moving object assignment problem, extending analysis to multiple dimensions and establishing optimality bounds.

Findings

Deterministic 1D algorithm with O(log ply) competitive ratio.

Randomized multi-dimensional algorithm with O(log ply) ratio.

Lower bounds proving no better ratios are possible.

Abstract

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.