TY - GEN
T1 - A discrepancy lower bound for information complexity
AU - Braverman, Mark
AU - Weinstein, Omri
PY - 2012
Y1 - 2012
N2 - This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also applies to information complexity. More precisely, if the discrepancy of a two-party function f with respect to a distribution μ is Disc μ f, then any two party randomized protocol computing f must reveal at least Ω(log(1/Disc μ f)) bits of information to the participants. As a corollary, we obtain that any two-party protocol for computing a random function on {0,1} n × {0,1} n must reveal Ω(n) bits of information to the participants. In addition, we prove that the discrepancy of the Greater-Than function is Ω(1/√n), which provides an alternative proof to the recent proof of Viola [Vio11] of the Ω(log n) lower bound on the communication complexity of this well-studied function and, combined with our main result, proves the tight Ω(log n) lower bound on its information complexity. The proof of our main result develops a new simulation procedure that may be of an independent interest. In a very recent breakthrough work of Kerenidis et al. [KLL +12], this simulation procedure was a building block towards a proof that almost all known lower bound techniques for communication complexity (and not just discrepancy) apply to information complexity.
AB - This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also applies to information complexity. More precisely, if the discrepancy of a two-party function f with respect to a distribution μ is Disc μ f, then any two party randomized protocol computing f must reveal at least Ω(log(1/Disc μ f)) bits of information to the participants. As a corollary, we obtain that any two-party protocol for computing a random function on {0,1} n × {0,1} n must reveal Ω(n) bits of information to the participants. In addition, we prove that the discrepancy of the Greater-Than function is Ω(1/√n), which provides an alternative proof to the recent proof of Viola [Vio11] of the Ω(log n) lower bound on the communication complexity of this well-studied function and, combined with our main result, proves the tight Ω(log n) lower bound on its information complexity. The proof of our main result develops a new simulation procedure that may be of an independent interest. In a very recent breakthrough work of Kerenidis et al. [KLL +12], this simulation procedure was a building block towards a proof that almost all known lower bound techniques for communication complexity (and not just discrepancy) apply to information complexity.
UR - http://www.scopus.com/inward/record.url?scp=84865294946&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-642-32512-0_39
DO - https://doi.org/10.1007/978-3-642-32512-0_39
M3 - منشور من مؤتمر
SN - 9783642325113
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 459
EP - 470
BT - Approximation, Randomization, and Combinatorial Optimization
T2 - 15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
Y2 - 15 August 2012 through 17 August 2012
ER -