A new distributed algorithm is presented which finds the shortest paths from every node in the network to a given destination node. The network topology is assumed to be organizable into a generalized balanced-tree hierarchy (BH). The BH toplogy is introduced and characterized in this paper, and it is shown that most large interconnected data networks belong to this class. Assuming one processor is available per node in an n node BH topology, the computation and communication time complexities of the proposed algorithm are O(logn) and O[(logn) 2], respectively. (Actually, a communication complexity of O(log n) can be achieved, but due to the space limit the description of this more sophisticated communication scheme is not included in this paper.) It is also shown that the algorithm converges in an asynchronous environment. Therefore, some of the difficulties associated with synchronizing the order of events can be avoided in the actual implementation of the proposed algorithm.