Communication complexity

About: Communication complexity is a research topic. Over the lifetime, 3870 publications have been published within this topic receiving 105832 citations.

Quantum vs. Classical Communication and Computation

Abstract: We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism. This allows us to obtain new positive and negative results. The positive results are novel quantum communication protocols that are built from nontrivial quantum algorithms via this simulation. These protocols, combined with (old and new) classical lower bounds, are shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) two-party communication complexity models. In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separation for the zero-error model. The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model. In particular, we show that the quadratic speed-up achieved by Grover for the OR function is impossible for the PARITY function or the MAJORITY function in the bounded-error model, nor is it possible for the OR function itself in the exact case. This dichotomy naturally suggests a study of bounded-depth predicates (i.e. those in the polynomial hierarchy) between OR and MAJORITY. We present black-box algorithms that achieve near quadratic speed up for all such predicates.

Proofs of Retrievability via Hardness Amplification

Abstract: Proofs of Retrievability (PoR) , introduced by Juels and Kaliski [JK07], allow the client to store a file F on an untrusted server, and later run an efficient audit protocol in which the server proves that it (still) possesses the client's data. Constructions of PoR schemes attempt to minimize the client and server storage, the communication complexity of an audit, and even the number of file-blocks accessed by the server during the audit. In this work, we identify several different variants of the problem (such as bounded-use vs. unbounded-use, knowledge-soundness vs. information-soundness), and giving nearly optimal PoR schemes for each of these variants. Our constructions either improve (and generalize) the prior PoR constructions, or give the first known PoR schemes with the required properties. In particular, we Formally prove the security of an (optimized) variant of the bounded-use scheme of Juels and Kaliski [JK07], without making any simplifying assumptions on the behavior of the adversary. Build the first unbounded-use PoR scheme where the communication complexity is linear in the security parameter and which does not rely on Random Oracles, resolving an open question of Shacham and Waters [SW08]. Build the first bounded-use scheme with information-theoretic security. The main insight of our work comes from a simple connection between PoR schemes and the notion of hardness amplification , extensively studied in complexity theory. In particular, our improvements come from first abstracting a purely information-theoretic notion of PoR codes , and then building nearly optimal PoR codes using state-of-the-art tools from coding and complexity theory.

Trading computation for bandwidth: reducing communication in distributed control systems using state estimators

Abstract: Describes a new framework for distributed control systems in which estimators are used at each node to estimate the values of the outputs at the other nodes. The estimated values are then used to compute the control algorithms at each node. When the estimated value deviates from the true value by more than a pre-specified tolerance, the actual value is broadcast to the rest of the system; all of the estimators are then updated to the current value. By using the estimated values instead of true value at every node, a significant saving in the required bandwidth is achieved, allowing large-scale distributed control systems to be implemented effectively. The stability, performance, and expected communication frequency of the reduced communication system are analyzed in detail. Simulation and experimental results validating the effectiveness and communication savings of the framework are also presented.