The cost of fault tolerance in multi-party communication complexity
Chen, B. Yu, H. Zhao, Y. Gibbons, P.B.
Chen, B.
Zhao, Y.
Gibbons, P.B.
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Abstract
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. UNIONSIZECP comes with a novel cycle promise, which is the key enabler of our reduction. We further prove that this cycle promise and UNIONSIZECP likely play a fundamental role in reasoning about fault-tolerant communication complexity. © 2012 ACM.
Keywords
aggregation functions, communication complexity, fault tolerance, promise problems, wireless networks
Source Title
Proceedings of the Annual ACM Symposium on Principles of Distributed Computing
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Date
2012
DOI
10.1145/2332432.2332442
Type
Conference Paper