This paper gives two simple efficient distributed algorithms: one for keeping clocks in a network synchronized and one for allowing new processors to join the network with their clocks synchronized. Assuming a fault-tolerant authentication protocol, the algorithms tolerate both link and processor failures of any type. The algorithm for maintaining synchronization works for arbitrary networks (rather than just completely connected networks) and tolerates any number of processor or communication link faults as long as the correct processors remain connected by fault-free paths. It thus represents an improvement over other clock synchronization algorithms such as those of Lamport and Melliar Smith and Welch and Lynch, although, unlike them, it does require an authentication protocol to handle Byzantine faults. Our algorithm for allowing new processors to join requires that more than half the processors be correct, a requirement that is provably necessary.

We model a communication network as a graph in which a processor is a node and a communication link is an edge. A routing for such a network is a fixed path, or route, between each pair of nodes. Given a network with a predefined routing, we study the effects of faulty components on the routing. Of particular interest is the number of routes along which a message must travel between any two non-faulty nodes. This problem is analyzed for specific families of graphs and for classes of routings. We also give some bounds for general versions of the problem. Finally, we conclude with one of the most important contributions of this paper, a list of interesting and apparently difficult open problems.

This paper gives two simple efficient distributed algorithms: one for keeping clocks in a network synchronized and one for allowing new processors to join the network with their clocks synchronized. The algorithms tolerate both link and node failures of any type. The algorithm for maintaining synchronization will work for arbitrary networks (rather than just completely connected networks) and tolerates any number of processor or communication link faults as long as the correct processors remain connected by fault-free paths. It thus represents an improvement over other clock synchronization algorithms such as [LM1,LM2,LL1]. Our algorithm for allowing new processors to join requires that more than half the processors be correct, a requirement which is provably necessary.