The Cost of Fault Tolerance in Multi-Party Communication Complexity

摘要

Multi-party communication complexity involves distributed computation of a function over inputs held by multiple distributed players. A key focus of distributed computing research, since the very beginning, has been to tolerate crash failures. It is thus natural to ask "If we want to compute a certain function in a fault-tolerant way, what will the communication complexity be?" This natural question, interestingly, has not been formally posed and thoroughly studied prior to this work. Whether fault-tolerant communication complexity is interesting to study largely depends on how big a difference failures make. This paper proves that the impact of failures is significant, at least for the SUM aggregation function in general networks: As our central contribution, we prove that there exists (at least) an exponential gap between the non-fault-tolerant and fault-tolerant communication complexity of Sum. Our results also imply the optimality (within polylog factors) of some recent fault-tolerant protocols for computing Sum via duplicate-insensitive techniques, thereby answering an open question as well. Part of our results are obtained via a novel reduction from a new two-party problem UnionSizeCP that we introduce. Union-SizeCP comes with a novel cycle promise, which is the key en-abler of our reduction. We further prove that this cycle promise and UnionSizeCP likely play a fundamental role in reasoning about fault-tolerant communication complexity.