In this paper, we present a routing algorithm for a class of dynamic networks called the Delay Tolerant Networks (DTNs). The proposed algorithm takes into account the quintessential DTN characteristic namely, intermittent link connectivity. We modify the breadth first search (BFS) algorithm to take into account link state changes and find the quickest route between source and destination nodes. We adopt a message drop policy at intermediate nodes to incorporate storage constraint. We also introduce the idea of time-varying storage domains where all nodes connected for a length of time act as a single storage unit by sharing the aggregated storage capacity of the nodes. We evaluate the routing algorithm with and without storage domain in an extensive simulation. We analyze the performance using metrics such as delivery ratio, incomplete transfers with no routes and dropped messages. The DTN topology dynamics are analyzed by varying: number of nodes generating traffic, link probability, link availability through combinations of downtime/uptime values, storage per node, message size, and traffic. The delay performance of the proposed algorithms is conceptually the same as flooding-based algorithms but without the penalty of multiple copies. More significantly, we show that the Quickest Storage Domain (Quickest SD) algorithm distributes the storage demand across many nodes in the network topology, enabling balanced load and higher network utilization. In fact, we show that for the same level of performance, we can actually cut the storage requirement in half using the Quickest SD algorithm.