On the Work Function Algorithm for two state task

We revisit the known work function online algorithm WFA for metrical task systems in the special case when there are only two states. We offer a slightly modified version of this algorithm, and show that our version exactly mimics the migration pattern of the best possible offline algorithm, though the timing of the migration events is somewhat different in these two algorithms. We use this to bound the cost of WFA in terms of the cost of the optimal offline algorithm. We show that our version of WFA not only has competitive ratio at most 3 in the worse case (which is best possible in the worst case), but additionally enjoys better competitive ratios on “typical” input sequences. We also present experimental evidence to support our theoretical analysis.