In systems biology, the solution space for a broad range of problems is composed of sets of functionally associated biomolecules. Since connectivity in molecular interaction networks is an indicator of functional association, such sets can be identified from connected induced subgraphs of molecular interaction networks. Applications typically quantify the relevance (e.g., modularity, conservation, disease association) of connected subnetworks using an objective function and use a search algorithm to identify sets of subnetworks that maximize this objective function. Efficient enumeration of connected subgraphs of a large graph is therefore useful for these applications, and many existing search algorithms can be used for this purpose. However, there is a lack of non-heuristic algorithms that minimize the total number of subgraphs evaluated during the search for subgraphs that maximize the objective function. In this talk, we describe and evaluate an algorithm that reduces the computations necessary to enumerate subgraphs that maximize an objective function given a monotonically decreasing bounding function.