Multi-Context Systems (MCS) are formalisms that enable the interlinkage of single knowledge bases, called contexts, via bridge rules. Recently, the evaluation of heterogeneous, nonmonotonic MCS was considered in Dao-Tran et al. (2010), where a fully distributed algorithm was described. In this paper, we continue this line of work and present a decomposition technique for MCS which analyzes the topology of an MCS. It applies pruning techniques to get economically small representations of context dependencies. Orthogonal to this, we characterize minimal interfaces for information exchange between contexts, such that data transmissions can be minimized. We then present a novel evaluation algorithm that operates on a query plan which is compiled with topology pruning and interface minimization. The effectiveness of the optimization techniques is demonstrated by a prototype implementation, which uses an off-the-shelf SAT solver and shows encouraging experimental results.