Uniform metrical task systems with a limited number of states

We give a randomized algorithm (the “Wedge Algorithm”) of competitiveness for any metrical task system on a uniform space of k points, for any k⩾2, where , the kth harmonic number. This algorithm has better competitiveness than the Irani–Seiden algorithm if k is smaller than 108. The algorithm is better by a factor of 2 if k<47.