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Filters: Author is Braverman, Mark  [Clear All Filters]
2019-12-10
Braverman, Mark, Kol, Gillat.  2018.  Interactive Compression to External Information. Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. :964-977.

We describe a new way of compressing two-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the participants' private inputs to an observer that watches the communication, can be simulated by a new protocol that communicates at most poly(I) $\cdot$ loglog(C) bits. Our result is tight up to polynomial factors, as it matches the recent work separating communication complexity from external information cost.

2017-10-03
Braverman, Mark, Efremenko, Klim, Gelles, Ran, Haeupler, Bernhard.  2016.  Constant-rate Coding for Multiparty Interactive Communication is Impossible. Proceedings of the Forty-eighth Annual ACM Symposium on Theory of Computing. :999–1010.

We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability ε. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise. Our main result is a lower bound on the communication of any noise-resilient protocol over a synchronous star network with n-parties (where all parties communicate in every round). Specifically, we show a task that can be solved by communicating T bits over the noise-free network, but for which any protocol with success probability of 1-o(1) must communicate at least Ω(T log n / log log n) bits when the channels are noisy. By a 1994 result of Rajagopalan and Schulman, the slowdown we prove is the highest one can obtain on any topology, up to a log log n factor. We complete our lower bound with a matching coding scheme that achieves the same overhead; thus, the capacity of (synchronous) star networks is Θ(log log n / log n). Our bounds prove that, despite several previous coding schemes with rate Ω(1) for certain topologies, no coding scheme with constant rate Ω(1) exists for arbitrary n-party noisy networks.