Distributed algorithms for unidirectional networks

This paper addresses the question of distributively computing over a strongly connected unidirectional data communication network. Algorithms for two basic problems in distributed computing, traversal and election, are provided. Each of these basic protocols produces two directed spanning trees rooted at a distinguished node in the network, one leading to the root and the other, from the root. Given these trees, the authors efficiently transform bidirectional algorithms to run on unidirectional networks, and in particular solve other problems such as broadcast and echo in a way that is more efficient than direct transformation. The communication cost of the traversal and election algorithms is O(nm + n² log n) bits (O(nm) messages and time), where m is the total number of links in the network. The traversal algorithm for unidirectional networks of finite automata achieve the same cost (O(nm + n² log n) bits) in the asynchronous case, while in the synchronous case the communication cost is O(nm) bits.