In our previous paper [1], we formalized an active information fusion framework based on dynamic Bayesian networks to provide active information fusion. This paper focuses on a central issue of active information fusion: efficient identification of a subset of sensors that are most decision-relevant and cost-effective. Determining the most informative and cost-effective sensors requires an evaluation of all possible subsets of sensors, which is computationally intractable, especially when information-theoretic criterion such as mutual information is used. To overcome this challenge, we propose a new quantitative measure for sensor synergy, based on which a sensor synergy graph is constructed. Using the sensor synergy graph, we first introduce an alternative measure to multi-sensor mutual information for characterizing sensor information gain, and we then propose an approximated nonmyopic sensor selection method that can efficiently and near-optimally select a subset of sensors for act...