Exponential Separation of Information and Communication

Ganor, Anat; Kol, Gillat; Raz, Ran

doi:10.1109/focs.2014.27

Cited by 44 publications

(38 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the parameters ∆s and N s that appear in the fudge parameters can be chosen as O(n 1/4 ). Specifically, by standard measure concentration bounds (for bounded random variables), for every ν > 0, there exists a constant 20 c > 0 such that with…”

Section: A Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

Information Complexity Density and Simulation of Protocols

Tyagi

Venkatakrishnan

Viswanath

et al. 2017

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Two parties observing correlated random variables seek to run an interactive communication protocol.How many bits must they exchange to simulate the protocol, namely to produce a view with a joint distribution within a fixed statistical distance of the joint distribution of the input and the transcript of the original protocol? We present an information spectrum approach for this problem whereby the information complexity of the protocol is replaced by its information complexity density. Our singleshot bounds relate the communication complexity of simulating a protocol to tail bounds for information complexity density. As a consequence, we obtain a strong converse and characterize the second-order asymptotic term in communication complexity for independent and identically distributed observation sequences. Furthermore, we obtain a general formula for the rate of communication complexity which applies to any sequence of observations and protocols. Connections with results from theoretical computer science and implications for the function computation problem are discussed.

show abstract

Section: A Proof Of Theoremmentioning

confidence: 99%

“…19 We use this notation throughout this section to avoid repetition. 20 Although the constant depends on random variables appearing in each round, since the number of rounds is bounded, we take the maximum constant so that (33) holds for every t.…”

Section: A Proof Of Theoremmentioning

confidence: 99%

Information Complexity Density and Simulation of Protocols

Tyagi

Venkatakrishnan

Viswanath

et al. 2017

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…This question has not been fully resolved yet, but the answer will have deep implications in theoretical computer science [7,3,15]. Both singleshot compression [3] and amortized cost in the limit [7] are of great interest, and they appear to have very different costs [15].…”

Section: Introductionmentioning

confidence: 98%

On Information Complexity in the Broadcast Model

Braverman

Oshman

2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

Information complexity is the extension of classical information theory to the interactive setting, where instead of one-way transmission we are interested in back-and-forth communication. This approach has been very influential in communication complexity, where it enables us to prove powerful lower bounds by quantifying the amount of information the participants in the computation must reveal about their inputs. In this paper we study information complexity in the classical broadcast model: k parties with private inputs wish to compute some function of their inputs, and they communicate by sending messages (one at a time) over a broadcast channel. We measure how much information the players reveal about their inputs to an external observer. This is called external information cost.Using this approach, we prove a tight lower bound of Ω(n log k+ k) on the communication complexity of set disjointness, a fundamental problem in communication complexity. We also give a deterministic matching upper bound.Next we study compression, a central question in information complexity: given a protocol with low information cost (but possibly high communication), can we compress the protocol so that its communication cost matches its information cost? In the twoplayer setting, it is known that every protocol can be compressed to roughly its external information cost. We show that for the multi-party case this is no longer true: there is a gap of at least Ω(k/ log k) between external information and communication. However, if we wish to compress many independent instances of the same protocol, then it is possible to do so with an amortized percopy cost that approaches the information cost as the number of copies goes to infinity.

show abstract

“…While the reduction incurs an exponential loss, this loss turns out to be tight [28,29]. We note that the resulting communication protocol always runs in 2 rounds.…”

Section: Information Complexity Vs Communication Complexity Our Nexmentioning

confidence: 99%

“…First and foremost, we would like to understand to what extent interactive computation can be compressed. The recent results of [28,29] show that it is not the case that for all f , IC (f, ε) = Ω (R(f, ε)). Moreover, more recently, it was also shown [30] that it is not the case that IC ext (f, ε) = Ω(R(f, ε))-at least for relations-and there is every reason to believe that it is not the case for functions either.…”

Section: Properties Of the Interactive Information Complexitymentioning

confidence: 99%

Interactive Information Complexity

Braverman¹

2017

SIAM Rev.

View full text Add to dashboard Cite

Abstract. The primary goal of this paper is to define and study the interactive information complexity of functions. Let f (x, y) be a function, and suppose Alice is given x and Bob is given y. Informally, the interactive information complexity IC(f ) of f is the least amount of information Alice and Bob need to reveal to each other to compute f . Previously, information complexity has been defined with respect to a prior distribution on the input pairs (x, y). Our first goal is to give a definition that is independent of the prior distribution. We show that several possible definitions are essentially equivalent. We establish some basic properties of the interactive information complexity IC(f ). In particular, we show that IC(f ) is equal to the amortized (randomized) communication complexity of f . We also show a direct sum theorem for IC(f ) and give the first general connection between information complexity and (nonamortized) communication complexity. This connection implies that a nontrivial exchange of information is required when solving problems that have nontrivial communication complexity. We explore the information complexity of two specific problems: equality and disjointness. We show that only a constant amount of information needs to be exchanged when solving equality with no errors, while solving disjointness with a constant error probability requires the parties to reveal a linear amount of information to each other. This paper originally appeared in [SIAM J. Comput., 44 (2015), pp. 1698-1739]. The present version has been slightly updated with some recent developments.

show abstract

Exponential Separation of Information and Communication

Cited by 44 publications

References 20 publications

Information Complexity Density and Simulation of Protocols

Information Complexity Density and Simulation of Protocols

On Information Complexity in the Broadcast Model

Interactive Information Complexity

Contact Info

Product

Resources

About