The k-Server Problem with Parallel Requests and the Compound Harmonic Algorithm

In this paper the (randomized) compound Harmonic algorithm for solving the generalized k-server problem is proposed. This problem is an online k-server problem with parallel requests where several servers can also be located on one point. In 2000 Bartal and Grove have proved that the well-known Harmonic algorithm is competitive for the (usual) k-server problem. Unfortunately, certain techniques of this proof cannot be used to show that a natural generalization of the Harmonic algorithm is competitive for the problem with parallel requests. The probabilities, which are used by the compound Harmonic algorithm are, finally, derived from a surrogate problem, where at most one server must be moved in servicing the request in each step. We can show that the compound Harmonic algorithm is competitive with the bound of the ratio as which has been proved by Bartal and Grove in the case of the usual problem.