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Electronic Colloquium on Computational Complexity

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Reports tagged with communication complexity:
TR16-168 | 2nd November 2016
Eric Blais, Clement Canonne, Tom Gur

Alice and Bob Show Distribution Testing Lower Bounds (They don't talk to each other anymore.)

Revisions: 1

We present a new methodology for proving distribution testing lower bounds, establishing a connection between distribution testing and the simultaneous message passing (SMP) communication model. Extending the framework of Blais, Brody, and Matulef [BBM12], we show a simple way to reduce (private-coin) SMP problems to distribution testing problems. This method ... more >>>

TR16-174 | 7th November 2016
Elchanan Mossel, Sampath Sampath Kannan, Grigory Yaroslavtsev

Linear Sketching over $\mathbb F_2$

Revisions: 5 , Comments: 2

We initiate a systematic study of linear sketching over $\mathbb F_2$. For a given Boolean function $f \colon \{0,1\}^n \to \{0,1\}$ a randomized $\mathbb F_2$-sketch is a distribution $\mathcal M$ over $d \times n$ matrices with elements over $\mathbb F_2$ such that $\mathcal Mx$ suffices for computing $f(x)$ with high ... more >>>

TR17-061 | 3rd April 2017
Anat Ganor, Karthik C. S.

Communication Complexity of Correlated Equilibrium in Two-Player Games

We show a communication complexity lower bound for finding a correlated equilibrium of a two-player game. More precisely, we define a two-player $N \times N$ game called the 2-cycle game and show that the randomized communication complexity of finding a 1/poly($N$)-approximate correlated equilibrium of the 2-cycle game is $\Omega(N)$. For ... more >>>

TR17-071 | 14th April 2017
Young Kun Ko, Arial Schvartzman

Bounds for the Communication Complexity of Two-Player Approximate Correlated Equilibria

Revisions: 1

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 >>>

TR17-151 | 8th October 2017
Paul Beame, Noah Fleming, Russell Impagliazzo, Antonina Kolokolova, Denis Pankratov, Toniann Pitassi, Robert Robere

Stabbing Planes

We introduce and develop a new semi-algebraic proof system, called Stabbing Planes that is in the style of DPLL-based modern SAT solvers. As with DPLL, there is only one rule: the current polytope can be subdivided by
branching on an inequality and its "integer negation.'' That is, we can (nondeterministically ... more >>>

TR17-170 | 6th November 2017
Arkadev Chattopadhyay, Michal Koucky, Bruno Loff, Sagnik Mukhopadhyay

Simulation Beats Richness: New Data-Structure Lower Bounds

We develop a technique for proving lower bounds in the setting of asymmetric communication, a model that was introduced in the famous works of Miltersen (STOC'94) and Miltersen, Nisan, Safra and Wigderson (STOC'95). At the core of our technique is a novel simulation theorem: Alice gets a $p \times n$ ... more >>>

TR17-177 | 16th November 2017
Daniel Kane, Roi Livni, Shay Moran, Amir Yehudayoff

On Communication Complexity of Classification Problems

Revisions: 1

This work introduces a model of distributed learning in the spirit of Yao's communication complexity model. We consider a two-party setting, where each of the players gets a list of labelled examples and they communicate in order to jointly perform some learning task. To naturally fit into the framework of ... more >>>

TR18-031 | 15th February 2018
Iftach Haitner, Noam Mazor, Rotem Oshman, Omer Reingold, Amir Yehudayoff

On the Communication Complexity of Key-Agreement Protocols

Key-agreement protocols whose security is proven in the random oracle model are an important alternative to the more common public-key based key-agreement protocols. In the random oracle model, the parties and the eavesdropper have access to a shared random function (an "oracle"), but they are limited in the number of ... more >>>

TR18-043 | 22nd February 2018
Andrei Romashchenko, Marius Zimand

An operational characterization of mutual information in algorithmic information theory

We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings
$x$ and $y$ is equal, up to logarithmic precision, to the length of the longest shared secret key that
two parties, one having $x$ and the complexity profile of the pair and the ... more >>>

TR18-079 | 19th April 2018
Jayadev Acharya, Clement Canonne, Himanshu Tyagi

Distributed Simulation and Distributed Inference

Independent samples from an unknown probability distribution $\mathbf{p}$ on a domain of size $k$ are distributed across $n$ players, with each player holding one sample. Each player can communicate $\ell$ bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a ... more >>>

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