Name
Abstract | ||
|---|---|---|
We describe new ways to simulate two-party communication protocols to get protocols with potentially less communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the inputs to the participating parties can be simulated by a new protocol involving at most (O) over tilde(root CI) bits of communication. If the protocol reveals I bits of information about the inputs to an observer that watches the communication in the protocol, we show how to carry out the simulation with (O) over tilde (I) bits of communication. These results lead to a direct sum theorem for randomized communication complexity. Ignoring polylogarithmic factors, we show that for worst-case computation, computing n copies of a function requires root n times the communication required for computing one copy of the function. For average case complexity, given any distribution mu on inputs, computing n copies of the function on n inputs sampled independently according to mu requires root n times the communication for computing one copy. If mu is a product distribution, computing n copies on n independent inputs sampled according to mu requires n times the communication required for computing the function. We also study the complexity of computing the sum (or parity) of n evaluations of f, and obtain results analogous to those above. Our results give the first compression schemes for general randomized protocols and the first direct sum results in the general setting of randomized and distributional communication complexity, without requiring bound on the number of rounds in the protocol or that the distribution of inputs is independent. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/100811969 | SIAM JOURNAL ON COMPUTING |
Keywords | Field | DocType |
interactive information,compression,communication complexity,direct sum | Information theory,Average-case complexity,Combinatorics,Computer science,Direct sum,Theoretical computer science,Communication complexity,Observer (quantum physics),Computation,Communications protocol,Fold (higher-order function) | Journal |
Volume | Issue | ISSN |
42 | 3 | 0097-5397 |
Citations | PageRank | References |
48 | 1.81 | 23 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Boaz Barak | 1 | 2563 | 127.61 |
| Mark Braverman | 2 | 810 | 61.60 |
| Xi Chen | 3 | 950 | 66.32 |
| Anup Rao | 4 | 581 | 32.80 |