Abstract-Most of the literature on delay tolerant networks (DTNs) focuses on optimal routing policies exploiting a priori knowledge about nodes mobility traces. For the case in which no a priori knowledge is available (very common in practice), apart from basic epidemic routing, the main approaches focus on controlling two-hop routing policies. However, these latter results commonly employ fluid approximation techniques, which, in principle, do not provide any theoretical bound over the approximation ratio. In our work, we focus on the case without a priori mobility knowledge and we provide approximation algorithms with theoretical guarantees that can be applied to cases where the number of hops allowed in the routing process is arbitrary. Our approach is rather flexible allowing us to address heterogeneous mobility patterns and transmission technologies, to consider explicitly the signaling and transmission costs, and to include also nodes discarding packets after a local timeout. We then provide a comprehensive performance evaluation of our algorithms, showing that two-hop routing provides the best tradeoff between delay and energy and that, in this case, they find solutions very close to the optimal ones with a low overhead. Finally, we compare our methods against some state-of-the-art approaches by means of a DTN simulation environment in realistic settings.