Brief Announcement: Deterministic Consensus and Checkpointing with Crashes: Time and Communication Efficiency

We study consensus and checkpointing in synchronous distributed systems. There are n nodes that communicate by sending messages, and any two nodes can communicate directly. The nodes are prone to crashing, with an upper bound t on the number of crashes. Algorithms use overlay networks of choice to save on the amount of communication. We explore using Ramanujan graphs as such overlay networks. We demonstrate that Ramanujan graphs have topological properties conducive to fault-tolerance and time/communication efficiency of distributed algorithms. Our consensus algorithm assumes binary input values, runs in O(t) time and sends O(n+t log t) bits. The algorithm sends the optimum number O(n) of bits for t=O(n/log n), thus for this range of t it improves on the algorithm by Galil, Mayer and Yung [FOCS 1995] that also sends O(n) bits but works in exponential time. The consensus algorithm can be implemented such that a node sends a message to at most one node at a round while maintaining the asymptotic time and communication performance bounds. Our checkpointing algorithm runs in linear time O(n) and with O(n log7 n) messages. It improves on the most communication-efficient and time-optimal algorithm by Galil, Mayer and Yung [FOCS 1995], which may have O(n1+) messages sent, for any chosen constant >0.