Direct Sums in Randomized Communication Complexity

by Boaz Barak, Mark Braverman, Anup Rao and Xi Chen.

Oded's comments

I would highlight more the new models and results regarding compressing any communication protocol at the protocol-level rather than the message level. Indeed, these models and results seem complementary to Schulman et al treatment of error-correction at the protocol level. Thus, these two models extend the classical treatments of compression and error-correction from the single message level to the protocol level.

The direct sum result follows by starting with a protocol for the $k$-wise problem, deriving a protocol for a single instance that has the same communication complexity but a low "information contents", and then reducing the communication complexity by using the new compression (at protocol level) scheme.

The original abstract

Does computing several copies of a function require more computational effort that computing a single copy? In this work, we give the first answers to this question for the model of randomized communication complexity. Ignoring logarithmic factors, we show that: Our results are obtained by designing compression schemes for communication protocols that can be used to compress the communication in a protocol that does not transmit a lot of information about its inputs.

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