Many emerging sensor network applications operate in challenging environments wherein the base station is not available. Data generated from such intermittently connected sensor networks (ICSNs) therefore must be stored inside the network for some unpredictable period of time before uploading opportunities become available. Consequently, sensory data could overflow the limited storage capacity available in the entire network, making discarding valuable data inevitable. To overcome such overall storage overflow in ICSNs, we propose and study a new algorithmic framework called data aggregation for overall storage overflow (DAO2). Utilizing spatial data correlation that commonly exists among sensory data, DAO2 employs data aggregation techniques to reduce the overflow data size while minimizing the total energy consumption in data aggregation. At the core of our framework are two new graph theoretical problems that have not been studied. We refer to them as traveling salesmen placement problem (TSP2) and quota traveling salesmen placement problem (Q-TSP2). Different from the well-known multiple traveling salesman problem (mTSP) and its variants, which mainly focus on the routing of multiple salesmen initially located at fixed locations, TSP2 and Q-TSP2 must decide the placement as well as the routing of the traveling salesmen. We prove that both problems are NP-hard and design approximation, heuristic, and distributed algorithms. Our algorithms outperform the state-of-the-art data aggregation work with base stations by up to 71.8% in terms of energy consumption. The building blocks of our framework are two novel graph structures called aggregation network and minimum q-edge forest that accurately capture the information needed for energy-efficient data aggregation in ICSNs.