Order-Preserving Renaming in Synchronous Systems with Byzantine Faults

Renaming is a fundamental problem in distributed computing. It consists in having a set of processes with unique ids from a large namespace pick distinct names from a smaller namespace. Order-preserving renaming is a stronger variant of the renaming problem where the new names are required to preserve the ordering of the initial ids. This paper addresses order-preserving renaming in synchronous message passing systems with Byzantine failures. Although in this model order-preserving renaming can be solved by using consensus, it is known that this problem is "weaker" than consensus. Therefore, we are interested in designing algorithms that are more efficient than consensus-based solutions. This paper makes three contributions in this direction. We present an order-preserving renaming algorithm with N > 3t resiliency, a target namespace of size N + t -- 1, and O(log N ) round complexity (N is the number of processes and t is an upper bound on the number of faults). We also show that with N > t2 +2t our algorithm can be modified to have constant round complexity while achieving tight namespace of size N. Finally, we present an algorithm that solves order-preserving renaming in just 2 communication rounds with N > 2t2 + t.