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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > DIRECT SUM:
Reports tagged with direct sum:
TR06-151 | 10th December 2006
Prahladh Harsha, Rahul Jain, David McAllester, Jaikumar Radhakrishnan

The communication complexity of correlation

We examine the communication required for generating random variables
remotely. One party Alice will be given a distribution D, and she
has to send a message to Bob, who is then required to generate a
value with distribution exactly D. Alice and Bob are allowed
to share random bits generated ... more >>>


TR09-044 | 6th May 2009
Boaz Barak, Mark Braverman, Xi Chen, Anup Rao

Direct Sums in Randomized Communication Complexity

Does computing n copies of a function require n times the computational effort? In this work, we

give the first non-trivial answer to this question for the model of randomized communication

complexity.

We show that:

1. Computing n copies of a function requires sqrt{n} times the ... more >>>


TR12-153 | 9th November 2012
Joshua Brody, Amit Chakrabarti, Ranganath Kondapally

Certifying Equality With Limited Interaction

Revisions: 1

The \textsc{equality} problem is usually one's first encounter with
communication complexity and is one of the most fundamental problems in the
field. Although its deterministic and randomized communication complexity
were settled decades ago, we find several new things to say about the
problem by focusing on two subtle aspects. The ... more >>>


TR13-079 | 2nd June 2013
Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

Direct Sum Fails for Zero Error Average Communication

We show that in the model of zero error communication complexity, direct sum fails for average communication complexity as well as for external information cost. Our example also refutes a version of a conjecture by Braverman et al. that in the zero error case amortized communication complexity equals external information ... more >>>


TR14-002 | 8th January 2014
Roee David, Irit Dinur, Elazar Goldenberg, Guy Kindler, Igor Shinkar

Direct Sum Testing

For a string $a \in \{0,1\}^n$ its $k$-fold direct sum encoding is a function $f_a$ that takes as input sets $S \subseteq [n]$ of
size $k$ and outputs $f_a(S) = \sum_{i \in S} a_i$.
In this paper we are interested in the Direct Sum Testing Problem,
where we are given ... more >>>


TR14-049 | 11th April 2014
Anat Ganor, Gillat Kol, Ran Raz

Exponential Separation of Information and Communication

Revisions: 1

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 >>>


TR14-113 | 27th August 2014
Anat Ganor, Gillat Kol, Ran Raz

Exponential Separation of Information and Communication for Boolean Functions

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 >>>


TR15-039 | 16th March 2015
Anup Rao, Makrand Sinha

On Parallelizing Streaming Algorithms

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 >>>


TR17-107 | 1st June 2017
Anurag Anshu, Dmitry Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal

A Composition Theorem for Randomized Query complexity

Revisions: 1

Let the randomized query complexity of a relation for error probability $\epsilon$ be denoted by $\R_\epsilon(\cdot)$. We prove that for any relation $f \subseteq \{0,1\}^n \times \mathcal{R}$ and Boolean function $g:\{0,1\}^m \rightarrow \{0,1\}$, $\R_{1/3}(f\circ g^n) = \Omega(\R_{4/9}(f)\cdot\R_{1/2-1/n^4}(g))$, where $f \circ g^n$ is the relation obtained by composing $f$ and $g$. ... more >>>


TR17-128 | 15th August 2017
Or Meir

The Direct Sum of Universal Relations

Revisions: 2 , Comments: 1

The universal relation is the communication problem in which Alice and Bob get as inputs two distinct strings, and they are required to find a coordinate on which the strings differ. The study of this problem is motivated by its connection to Karchmer-Wigderson relations, which are communication problems that are ... more >>>




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