  A new model of causal failure is presented and used to solve a novel replica
placement problem in data centers. The model describes dependencies among
system components as a directed graph. A replica placement is defined as a
subset of vertices in such a graph. A criterion for optimizing replica
placements is formalized and explained. In this work, the optimization goal is
to avoid choosing placements in which a single failure event is likely to wipe
out multiple replicas. Using this criterion, a fast algorithm is given for the
scenario in which the dependency model is a tree. The main contribution of the
paper is an $O(n + \rho \log \rho)$ dynamic programming algorithm for placing
$\rho$ replicas on a tree with $n$ vertices. This algorithm exhibits the
interesting property that only two subproblems need to be recursively
considered at each stage. An $O(n^2 \rho)$ greedy algorithm is also briefly
reported.
