Interactive Information Complexity

Braverman, Mark

doi:10.1137/17m1139254

Cited by 10 publications

(14 citation statements)

References 72 publications

(118 reference statements)

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“…It is not difficult to extend the compression protocol from [7] (which is designed for a different notion of information cost, internal information [4]) to the external information of protocols in the k-party broadcast model, obtaining the following result: 2 Compressing a protocol Π to some cost T means constructing another protocol Θ, whose communication complexity is T , such that given inputs X, Y , the players can use Θ to sample from a distribution close to the distribution of Π's transcript Π(X, Y ). The players are not charged for writing out the transcript of Π that they sampled, only for the communication they exchange in order to agree on the sample.…”

Section: Amortized Compressionmentioning

confidence: 99%

On Information Complexity in the Broadcast Model

Braverman

Oshman

2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

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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.

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Section: Amortized Compressionmentioning

confidence: 99%

On Information Complexity in the Broadcast Model

Braverman

Oshman

2015

Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing

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“…Thus ∀ α > 0, and for sufficiently large n, IC U (GH D n,n/2, √ n , ρ) ≤ αn. We will need the following theorem from [5,8]:…”

Section: Formal Proof Of Lemma 34mentioning

confidence: 99%

Information Lower Bounds via Self-Reducibility

et al. 2015

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We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the (n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of I P n is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the (n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702-732 2004;Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner.

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“…bits of communication was given in [10]. A general version of the simulation problem was considered in [55], but only bounded round simulation protocols were considered.…”

Section: Introductionmentioning

confidence: 99%

Information Complexity Density and Simulation of Protocols

Tyagi

Venkatakrishnan

Viswanath

et al. 2017

IEEE Trans. Inform. Theory

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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.

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Interactive Information Complexity

Cited by 10 publications

References 72 publications

On Information Complexity in the Broadcast Model

On Information Complexity in the Broadcast Model

Information Lower Bounds via Self-Reducibility

Information Complexity Density and Simulation of Protocols

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