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Summary: How to Compress Interactive Communication
Boaz Barak
Mark Braverman
Xi Chen
Anup Rao§
November 10, 2009
Abstract
We describe new ways to simulate 2-party communication protocols to get protocols with
potentially smaller communication. We show that every communication protocol that commu-
nicates C bits and reveals I bits of information to the participating parties can be simulated by
a new protocol involving at most ~O(
CI) bits of communication. In the case that the parties
have inputs that are independent of each other, we get much better results, showing how to
carry out the simulation with ~O(I) bits of communication.
These results lead to a direct sum theorem for randomized communication complexity. Ig-
noring polylogarithmic factors, we show that for worst case computation, computing n copies
of a function requires
n times the communication required for computing on copy of the func-
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