E. Koutsoupias.

**Weak adversaries for the k-server problem.**In*Proceedings of the 40th Annual Symposium on Foundations of Computer Science*, New York City, NY, pages 444--449, 17--19 October 1999.### 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.### Bib

@string{FOCS99 = {Proceedings of the 40th Annual Symposium on Foundations of Computer Science}} @InProceedings{Kou99, author = {E. Koutsoupias}, title = {Weak adversaries for the $k$-server problem}, booktitle = FOCS99, year = 1999, month = {17--19 } # oct, pages = {444--449}, address = {New York City, NY}, }