Abstract. We consider Dynamic Page Migration (DPM) problem, one of the fundamental subproblems of data management in dynamically changing networks. We investigate a hybrid scenario, where access patterns to the shared object are dictated by an adversary, and each processor performs a random walk in X. We extend the previous results of [4]: we develop algorithms for the case where X is a ring, and prove that with high probability they achieve a competitive ratio of Õ(min { 4 √ D, n}), where D is the size of the shared object and n is the number of nodes in the network. These results hold also for any d-dimensional torus or mesh with diameter at least ˜ Ω ( √ D). 1

In the last couple of decades, network connected systems have gradually replaced centralized parallel computing machines. To provide smooth operation of network applications, the underlying system has to provide so-called basic services. One of the most crucial services is to provide a transparent access to data like

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