On Space Bounded Server Algorithms

This paper studies space bounded algorithms, i.e., algorithms that use a constant amount of scratch space, for the k{server problem. The paper rst shows a characterization of the set of space bounded algorithms that are competitive in nite metric spaces. The result yields a method for (1) e ectively deciding if a given space bounded algorithm is competitive in a given nite metric space, and (2) for designing competitive space bounded algorithms in nite metric spaces. The above results are then re ned, in particular using the geometry of metric spaces, to develop two methods for obtaining an upper bound on competitive factors of arbitrary space bounded algorithms. One of these methods is then used to show that any algorithm, employing the Least Recently Used strategy, is linearly competitive on a uniform metric space.