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(rho) of the Work Function Algorithm. The first upper bound is k*opt_h(rho)+(h-1)*opt_k(rho)$, where opt_m(rho) denotes the optimal cost to service rho by m servers. The second upper bound is 2*h*opt_h(rho)-opt_k(rho) for h<=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.

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