We consider the task of multiparty computation performed over networks in the presence of random noise. Given an n-party protocol that takes R rounds assuming noiseless communication, the goal is to find a coding scheme that takes R′ rounds and computes the same function with high probability even when the communication is noisy, while maintaining a constant asymptotic rate, i.e., while keeping lim infn,R→∞ R/R′ positive. Rajagopalan and Schulman (STOC '94) were the first to consider this question, and provided a coding scheme with rate O(1= log(d + 1)), where d is the maximal degree in the network. While that scheme provides a constant rate coding for many practical situations, in the worst case, e.g., when the network is a complete graph, the rate is O(1= log n), which tends to 0 as n tends to infinity. We revisit this question and provide an efficient coding scheme with a constant rate for the interesting case of fully connected networks. We furthermore extend the result and show that if a (d-regular) network has mixing time m, then there exists an efficient coding scheme with rate O(1/m3 logm). This implies a constant rate coding scheme for any n-party protocol over a d-regular network with a constant mixing time, and in particular for random graphs with n vertices and degrees nω(1).
|Title of host publication
|PODC 2016 - Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing
|Association for Computing Machinery
|Number of pages
|Published - 25 Jul 2016
|35th ACM Symposium on Principles of Distributed Computing, PODC 2016 - Chicago, United States
Duration: 25 Jul 2016 → 28 Jul 2016
|Proceedings of the Annual ACM Symposium on Principles of Distributed Computing
|35th ACM Symposium on Principles of Distributed Computing, PODC 2016
|25/07/16 → 28/07/16
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