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A fundamental problem of distributed database design in an existing network where components can fail is finding an optimal location at which to place the database in a centralized system or copies of each data item in a decentralized or replicated system. In this paper it is proved for the first time exactly how hard this placement problem is under the measure of data availability. Specifically, we show that the optimal placement problem for availability is #P- complete, a measure of intractability at least as severe as NP-completeness. Given the anticipated computational difficulty of finding an exact solution, we go on to describe an effective, practical method for approximating the optimal copy placement. To obtain these results, we model the environment in which a distributed database operates by a probabilistic graph, which is a set of fully-reliable vertices representing sites, and a set of edges representing communication links, each operational with a rational probability. We prove that finding the optimal copy placement in a probabilistic graph is #P-complete by giving a sequence of reductions from #Satisfiability. We generalize this result to networks in which each site and each link has an independent, rational operational probability and to networks in which all the sites or all the links have a fixed, uniform operational probabilities.
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Donald B. Johnson and Larry Raab, "Complexity of Network Reliability and Optimal Database Placement Problems." Dartmouth Computer Science Technical Report PCS-TR91-167, 1991.
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