Weak adversaries for the k-server problem

We study the k-server problem when the offline algorithm has fewer than k servers. We give two upper bounds of the cost WFA(/spl rho/) of the Work Function Algorithm. The first upper bound is kOPT/sub h/(/spl rho/)+(h-1)OPT/sub k/(/spl rho/), where OPT/sub m/(/spl rho/) denotes the optimal cost to service /spl rho/ by m servers. The second upper bound is 2hOPTh(/spl rho/)-OPT/sub k/(/spl rho/) for h/spl les/k. Both bounds imply that the Work Function Algorithm is (2k-1)-competitive. Perhaps more important is our technique which seems promising for settling the k-server conjecture. The proofs are simple and intuitive and they do not involve potential functions. We also apply the technique to give a simple condition for the Work Function Algorithm to be k-competitive; this condition results in a new proof that the k-server conjecture holds for k=2.