A Tight Lower Bound for Processor Coordination

Abstract

We prove a tight lower bound on the running time of oblivious solutions to k-set agreement. Ink-set agreementprocessors start with input values from a given set and choose output values from the same set. In every execution, the set of output values must be contained in the set of input values, and the set of output values must have size at mostk.A solution isobliviousif it does not make use of processor identities. We analyze this problem in a synchronous model where processors can fail by just stopping. We prove a lower bound of [ilk] + 1 rounds of communication for oblivious solutions that tolerateffailures. This shows that there is an inherent tradeoff between the running time, the degree of coordination required, and the number of faults tolerated, even in idealized models like ours.