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This paper derives the optimal search time and the optimal search cost that can be achieved in unstructured peer-to-peer networks when the demand pattern exhibits clustering (i.e. file popularities vary across the set of nodes in the network). Clustering in file popularity patterns is evident from measurements on deployed peer-to-peer file sharing networks. In this paper, we provide mechanisms for modeling clustering in file popularity distributions and the consequent non-uniform distribution of file replicas. We derive relations that show the effect of the number of replicas of a file on the search time and on the search cost for a search for that file for the clustered demands case in such networks for both random walk and flooding search mechanisms. The derived relations are used to obtain the optimal search performance for the case of flooding search mechanisms. The potential performance benefit that clustering in demand patterns affords is captured by our results. Interestingly, the performance gains are shown to be independent of whether the search network topology reflects the clustering in file popularity (the optimal file replica distribution to obtain these performance gains, however, does depend on the search network topology).
Date of Publication: Jan. 2007