Weak adversaries for the k-server problem (Extended Abstract)

We study the k-server problem when the off-line algorithm has fewer than k servers. We give two upper bounds of the cost WFA(ae) of the Work Function Algorithm. The first upper bound is kOPT h (ae)+(h\Gamma1)OPT k (ae), where OPTm (ae) denotes the optimal cost to service ae by m servers. The second upper bound is 2hOPT h (ae) \Gamma OPT k (ae) for h k. Both bounds imply that the Work Function Algorithm is (2k \Gamma 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