Mark Braverman

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 ... more >>>

Mark Braverman, Ankur Moitra

We prove an unconditional lower bound that any linear program that achieves an $O(n^{1-\epsilon})$ approximation for clique has size $2^{\Omega(n^\epsilon)}$. There has been considerable recent interest in proving unconditional lower bounds against any linear program. Fiorini et al proved that there is no polynomial sized linear program for traveling salesman. ... more >>>

Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

We develop a new local characterization of the zero-error information complexity function for two party communication problems, and use it to compute the exact internal and external information complexity of the 2-bit AND function: $IC(AND,0) = C_{\wedge}\approx 1.4923$ bits, and $IC^{ext}(AND,0) = \log_2 3 \approx 1.5839$ bits. This leads to ... more >>>

Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

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 ... more >>>

Iordanis Kerenidis, Mathieu Laurière, David Xiao

Communication complexity is a central model of computation introduced by Yao in 1979, where

two players, Alice and Bob, receive inputs x and y respectively and want to compute $f(x; y)$ for some fixed

function f with the least amount of communication. Recently people have revisited the question of the ...
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Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

We obtain a strong direct product theorem for two-party bounded round communication complexity.

Let suc_r(\mu,f,C) denote the maximum success probability of an r-round communication protocol that uses

at most C bits of communication in computing f(x,y) when (x,y)~\mu.

Jain et al. [JPY12] have recently showed that if

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Mark Braverman, Ankit Garg

We precisely characterize the role of private randomness in the ability of Alice to send a message to Bob while minimizing the amount of information revealed to him. We show that if using private randomness a message can be transmitted while revealing $I$ bits of information, the transmission can be ... more >>>

Mark Braverman, Omri Weinstein

We introduce a novel technique which enables two players to maintain an estimate of the internal information cost of their conversation in an online fashion without revealing much extra information. We use this construction to obtain new results about communication complexity and information-theoretically secure computation.

As a first corollary, ... more >>>

Anat Ganor, Gillat Kol, Ran Raz

We show an exponential gap between communication complexity and information complexity, by giving an explicit example for a communication task (relation), with information complexity $\leq O(k)$, and distributional communication complexity $\geq 2^k$. This shows that a communication protocol cannot always be compressed to its internal information. By a result of ... more >>>

Alexander Kozachinsky

We prove a version of "Reversed Newman Theorem" in context of information complexity: every private-coin communication protocol with information complexity $I$ and communication complexity $C$ can be replaced by public-coin protocol with the same behavior so that it's information complexity does not exceed $O\left(\sqrt{IC}\right)$. This result holds for unbounded-round communication ... more >>>

Anat Ganor, Gillat Kol, Ran Raz

We show an exponential gap between communication complexity and information complexity for boolean functions, by giving an explicit example of a partial function with information complexity $\leq O(k)$, and distributional communication complexity $\geq 2^k$. This shows that a communication protocol for a partial boolean function cannot always be compressed to ... more >>>

Mark Braverman, Jieming Mao

We show that $T$ rounds of interaction over the binary symmetric channel $BSC_{1/2-\epsilon}$ with feedback can be simulated with $O(\epsilon^2 T)$ rounds of interaction over a noiseless channel. We also introduce a more general "energy cost'' model of interaction over a noisy channel. We show energy cost to be equivalent ... more >>>

Mark Braverman, Jon Schneider

The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary function $f$ to within any additive error $\alpha>0$, thus resolving an ... more >>>

Lila Fontes, Rahul Jain, Iordanis Kerenidis, Sophie Laplante, Mathieu Laurière, Jérémie Roland

Does the information complexity of a function equal its communication complexity? We examine whether any currently known techniques might be used to show a separation between the two notions. Recently, Ganor et al. provided such a separation in the distributional setting for a specific input distribution ?. We show that ... more >>>

Anup Rao, Makrand Sinha

We study the complexity of parallelizing streaming algorithms (or equivalently, branching programs). If $M(f)$ denotes the minimum average memory required to compute a function $f(x_1,x_2, \dots, x_n)$ how much memory is required to compute $f$ on $k$ independent streams that arrive in parallel? We show that when the inputs (updates) ... more >>>

Sivaramakrishnan Natarajan Ramamoorthy, Anup Rao

We study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If $I^A$ denotes the number of bits of information revealed by the first party, $I^B$ denotes the information revealed by the second party, and $C$ is the number of bits of communication in ... more >>>

Omri Weinstein

Information complexity is the interactive analogue of Shannon's classical information theory. In recent years this field has emerged as a powerful tool for proving strong communication lower bounds, and for addressing some of the major open problems in communication complexity and circuit complexity. A notable achievement of information complexity is ... more >>>

Himanshu Tyagi, Shaileshh Venkatakrishnan , Pramod Viswanath, Shun Watanabe

A simulation of an interactive protocol entails the use of an interactive communication to produce the output of the protocol to within a fixed statistical distance $\epsilon$. Recent works in the TCS community have propagated that the information complexity of the protocol plays a central role in characterizing the minimum ... more >>>

Omri Weinstein, David Woodruff

We study $k$-party set disjointness in the simultaneous message-passing model, and show that even if each element $i\in[n]$ is guaranteed to either belong to all $k$ parties or to at most $O(1)$ parties in expectation (and to at most $O(\log n)$ parties with high probability), then $\Omega(n \min(\log 1/\delta, \log ... more >>>

Badih Ghazi, Pritish Kamath, Madhu Sudan

Motivated by the quest for a broader understanding of communication complexity of simple functions, we introduce the class of ''permutation-invariant'' functions. A partial function $f:\{0,1\}^n \times \{0,1\}^n\to \{0,1,?\}$ is permutation-invariant if for every bijection $\pi:\{1,\ldots,n\} \to \{1,\ldots,n\}$ and every $\mathbf{x}, \mathbf{y} \in \{0,1\}^n$, it is the case that $f(\mathbf{x}, \mathbf{y}) ... more >>>

Anat Ganor, Gillat Kol, Ran Raz

We show an exponential gap between communication complexity and external information complexity, by analyzing a communication task suggested as a candidate by Braverman [Bra13]. Previously, only a separation of communication complexity and internal information complexity was known [GKR14,GKR15].

More precisely, we obtain an explicit example of a search problem with ... more >>>

Eli Ben-Sasson, Gal Maor

In this paper three complexity measures are studied: (i) internal information, (ii) external information, and (iii) a measure called here "output information". Internal information (i) measures the counter-party privacy-loss inherent in a communication protocol. Similarly, the output information (iii) measures the reduction in input-privacy that is inherent when the output ... more >>>

Alexander A. Sherstov

We study the problem of compressing interactive communication to its

information content $I$, defined as the amount of information that the

participants learn about each other's inputs. We focus on the case when

the participants' inputs are distributed independently and show how to

compress the communication to $O(I\log^{2}I)$ bits, with ...
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Yuval Dagan, Yuval Filmus, Hamed Hatami, Yaqiao Li

We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$.

For arbitrary functions, we obtain lower bounds and upper bounds indicating a gain that is of order $\Omega(h(\epsilon))$ and $O(h(\sqrt{\epsilon}))$. ...
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Young Kun Ko, Arial Schvartzman

In the recent paper of~\cite{BR16}, the authors show that, for any constant $10^{-15} > \varepsilon > 0$ the communication complexity of $\varepsilon$-approximate Nash equilibria in $2$-player $n \times n$ games is $n^{\Omega(\varepsilon)}$, resolving the long open problem of whether or not there exists a polylogarithmic communication protocol. In this paper ... more >>>

Badih Ghazi, T.S. Jayram

We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This problem is at the core of secret key generation in cryptography, with ... more >>>

Siddharth Iyer, Anup Rao

We define the marginal information of a communication protocol, and use it to prove XOR lemmas for communication complexity. We show that if every $C$-bit protocol has bounded advantage for computing a Boolean function $f$, then every $\tilde \Omega(C \sqrt{n})$-bit protocol has advantage $\exp(-\Omega(n))$ for computing the $n$-fold xor $f^{\oplus ... more >>>