Tentative and definite distributed computations: an optimistic approach to network synchronization

Abstract

We present here a general and efficient strategy for simulating a synchronous network by a network of limited asynchrony. Our proposed synchronizer is optimistic in the sense that it uses very efficient but tentative protocols to simulate a contiguous block of synchronous steps. However, since a tentative execution does not guarantee correct simulation, we audit the computation at selected points. The audits are used to check whether the computation of the block can be certified to be correct. We show that a wide class of networks of limited asynchrony admits practical tentative protocols which are highly likely to produce a correct simulation of one step with very small overhead. For those networks, the synchronizer exhibits a trade off between its communication and time complexities which is below the lower bounds for deterministic synchronizers. On one extreme the amortized complexity of our synchronizer is O(1) messages and O( log n) time (expected) per “step” of the simulated synchronous protocol. On other extreme the communication complexity is O( e Δ 2 ) and the time complexity is O( log Δ), for networks with e edges and maximum degree Δ.