Distributed Algorithms for Unidirectional Networks

We address the question of distributively computing over a strongly connected unidirectional data communication network. In unidirectional networks the existence of a communication link from one node to another does not imply the existence of a link in the opposite direction. The strong connectivity means that from every node there is a directed path to any other node. We assume an arbitrary topology network in which the strong connectivity is the only restriction. Four models are considered: Synchronous and asynchronous, and for each we consider node space availability which grows as either O(1) bits or O(log n) bits per incident link, where n is the total number of nodes in the network. First we provide algorithms for two basic problems in distributed computing in data communication networks, traversal, and election. Each of these basic protocols produces two directed spanning trees rooted at a distinguished node in the network, one called in-tree, leading to the root, and the other out-tree, leading from the root. Given these trees we eeciently transform bidirectional algorithms to run on unidirec-tional networks, and in particular solve other problems such as the broadcast and echo Cha79] in a way which is more eecient (O(n 2) messages) than direct transformation (that yield O(nm) messages algorithm). The communication cost of our traversal and election algorithms are both O(nm + n 2 log n) bits (O(nm) messages and time), where m is the total number of links in the network. The traversal algorithms for unidirec-tional networks of nite automata, achieve the same cost (O(nm + n 2 log n) bits) in the asynchronous case, while in the synchronous case the communication cost of our algorithm is O(mn) bits.