Unfair Problems and Randomized Algorithms for Metrical Task Systems

Borodin, Linial, and Saks introduce a general model for online systems in [Borodin et al. 1992] called metrical task systems. In this paper, the unfair two state problem, a natural generalization of the two state metrical task system problem, is studied. A randomized algorithm for this problem is presented, and it is shown that this algorithm is optimal. Using the analysis of unfair two state problem, a proof of a decomposition theorem similar to that of Blum, Karlo , Rabani and Saks [Blum et al. 1992] is presented. This theorem allows one to design divide and conquer algorithms for speci c metrical task systems. Our theorem gives the same bounds asymptotically, but has less restrictive boundary conditions. 4