Virtual Ring Construction in Parallel Distributed Systems

Many distributed systems and applications use decentralized control algorithms lying on a predefined virtual ring. Such a structure is usually statically defined, and is thus inherent to the system definition. Ring construction distributed algorithms are proposed. First, distributed depth-first traversal algorithms are shown to be an algorithmic basis for the construction of such a structure. Then, a ring construction algorithm is presented; its time and message complexities are equal to 2(n − 1) with O(n) size of messages, where n is the number of processes. A ring traversal requires 2(n−1) messages. This algorithm is then improved: it allows building of a virtual ring whose traversal requires p messages, where n ≤ p ≤ 2(n− 1).