Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > AUTHORS > MARK BRAVERMAN:
All reports by Author Mark Braverman:

TR17-182 | 21st November 2017
Mark Braverman, Young Kun Ko

Information Value of Two-Prover Games

We introduce a generalization of the standard framework for studying the difficulty of two-prover games. Specifically, we study the model where Alice and Bob are allowed to communicate (with information constraints) --- in contrast to the usual two-prover game where they are not allowed to communicate after receiving their respective ... more >>>


TR17-161 | 30th October 2017
Mark Braverman, Gil Cohen, Sumegha Garg

Hitting Sets with Near-Optimal Error for Read-Once Branching Programs

Nisan (Combinatorica'92) constructed a pseudorandom generator for length $n$, width $n$ read-once branching programs (ROBPs) with error $\varepsilon$ and seed length $O(\log^2{n} + \log{n} \cdot \log(1/\varepsilon))$. A major goal in complexity theory is to reduce the seed length, hopefully, to the optimal $O(\log{n}+\log(1/\varepsilon))$, or to construct improved hitting sets, as ... more >>>


TR16-166 | 1st November 2016
Mark Braverman, Ran Gelles, Michael A. Yitayew

Optimal Resilience for Short-Circuit Noise in Formulas

Revisions: 1

We show an efficient method for converting a logic circuit of gates with fan-out 1 into an equivalent circuit that works even if some fraction of its gates are short-circuited, i.e., their output is short-circuited to one of their inputs. Our conversion can be applied to any circuit with fan-in ... more >>>


TR15-197 | 7th December 2015
Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

Constant-rate coding for multiparty interactive communication is impossible

We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability $\epsilon$. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise.

Our ... more >>>


TR15-081 | 12th May 2015
Mark Braverman, Ankit Garg, Young Kun Ko, Jieming Mao, Dave Touchette

Near-optimal bounds on bounded-round quantum communication complexity of disjointness

We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with $r$ rounds, we prove a lower bound of $\tilde{\Omega}(n/r)$ on the communication required for computing disjointness of input size $n$, which is optimal up to logarithmic factors. The previous best lower bound ... more >>>


TR15-074 | 29th April 2015
Mark Braverman, Young Kun Ko, Aviad Rubinstein, Omri Weinstein

ETH Hardness for Densest-$k$-Subgraph with Perfect Completeness

We show that, assuming the (deterministic) Exponential Time Hypothesis, distinguishing between a graph with an induced $k$-clique and a graph in which all $k$-subgraphs have density at most $1-\epsilon$, requires $n^{\tilde \Omega(log n)}$ time. Our result essentially matches the quasi-polynomial algorithms of Feige and Seltser [FS97] and Barman [Bar15] for ... more >>>


TR15-023 | 10th February 2015
Mark Braverman, Jon Schneider

Information complexity is computable

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 >>>


TR15-014 | 18th January 2015
Noga Alon, Mark Braverman, Klim Efremenko, Ran Gelles, Bernhard Haeupler

Reliable Communication over Highly Connected Noisy Networks

We consider the task of multiparty computation performed over networks in
the presence of random noise. Given an $n$-party protocol that takes $R$
rounds assuming noiseless communication, the goal is to find a coding
scheme that takes $R'$ rounds and computes the same function with high
probability even when the ... more >>>


TR15-002 | 2nd January 2015
Mark Braverman, Rotem Oshman

The Communication Complexity of Number-In-Hand Set Disjointness with No Promise

Set disjointness is one of the most fundamental problems in communication complexity. In the multi-party number-in-hand version of set disjointness, $k$ players receive private inputs $X_1,\ldots,X_k\subseteq \{1,\ldots,n\}$, and their goal is to determine whether or not $\bigcap_{i = 1}^k X_i = \emptyset$. In this paper we prove a tight lower ... more >>>


TR14-119 | 15th September 2014
Mark Braverman, Jieming Mao

Simulating Noisy Channel Interaction

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 >>>


TR14-095 | 24th July 2014
Mark Braverman, Ankit Garg

Small value parallel repetition for general games

Revisions: 1

We prove a parallel repetition theorem for general games with value tending to 0. Previously Dinur and Steurer proved such a theorem for the special case of projection games. We use information theoretic techniques in our proof. Our proofs also extend to the high value regime (value close to 1) ... more >>>


TR14-092 | 22nd July 2014
Mark Braverman, Young Kun Ko, Omri Weinstein

Approximating the best Nash Equilibrium in $n^{o(\log n)}$-time breaks the Exponential Time Hypothesis

The celebrated PPAD hardness result for finding an exact Nash equilibrium in a two-player game
initiated a quest for finding \emph{approximate} Nash equilibria efficiently, and is one of the major open questions in algorithmic game theory.

We study the computational complexity of finding an $\eps$-approximate Nash equilibrium with good social ... more >>>


TR14-047 | 8th April 2014
Mark Braverman, Omri Weinstein

An Interactive Information Odometer with Applications

Revisions: 1

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 >>>


TR14-013 | 30th January 2014
Mark Braverman, Kanika Pasricha

The computational hardness of pricing compound options

It is generally assumed that you can make a financial asset out of any underlying event or combination thereof, and then sell a security. We show that while this is theoretically true from the financial engineering perspective, compound securities might be intractable to price. Even given no information asymmetries, or ... more >>>


TR14-007 | 17th January 2014
Mark Braverman, Klim Efremenko

List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise

In this paper we extend the notion of list decoding to the setting of interactive communication and study its limits. In particular, we show that any protocol can be encoded, with a constant rate, into a list-decodable protocol which is resilient
to a noise rate of up to $1/2-\varepsilon$, ... more >>>


TR13-130 | 17th September 2013
Mark Braverman, Ankit Garg

Public vs private coin in bounded-round information

Revisions: 1

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 >>>


TR13-035 | 6th March 2013
Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

Direct product via round-preserving compression

Revisions: 1

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
more >>>


TR12-177 | 19th December 2012
Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

Information lower bounds via self-reducibility

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 >>>


TR12-171 | 3rd December 2012
Mark Braverman, Ankit Garg, Denis Pankratov, Omri Weinstein

From Information to Exact Communication

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 >>>


TR12-143 | 5th November 2012
Mark Braverman, Anup Rao, Omri Weinstein, Amir Yehudayoff

Direct Products in Communication Complexity

Revisions: 2

We give exponentially small upper bounds on the success probability for computing the direct product of any function over any distribution using a communication protocol. Let suc(?,f,C) denote the maximum success probability of a 2-party communication protocol for computing f(x,y) with C bits of communication, when the inputs (x,y) are ... more >>>


TR12-131 | 18th October 2012
Mark Braverman, Ankur Moitra

An Information Complexity Approach to Extended Formulations

Revisions: 1

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 >>>


TR11-164 | 9th December 2011
Mark Braverman, Omri Weinstein

A discrepancy lower bound for information complexity

This paper provides the first general technique for proving information lower bounds on two-party
unbounded-rounds communication problems. We show that the discrepancy lower bound, which
applies to randomized communication complexity, also applies to information complexity. More
precisely, if the discrepancy of a two-party function $f$ with respect ... more >>>


TR11-123 | 15th September 2011
Mark Braverman

Interactive information complexity

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 >>>


TR11-064 | 23rd April 2011
Mark Braverman

Towards deterministic tree code constructions

We present a deterministic operator on tree codes -- we call tree code product -- that allows one to deterministically combine two tree codes into a larger tree code. Moreover, if the original tree codes are efficiently encodable and decodable, then so is their product. This allows us to give ... more >>>


TR10-166 | 5th November 2010
Mark Braverman, Anup Rao

Towards Coding for Maximum Errors in Interactive Communication

We show that it is possible to encode any communication protocol
between two parties so that the protocol succeeds even if a $(1/4 -
\epsilon)$ fraction of all symbols transmitted by the parties are
corrupted adversarially, at a cost of increasing the communication in
the protocol by a constant factor ... more >>>


TR10-083 | 13th May 2010
Mark Braverman, Anup Rao

Efficient Communication Using Partial Information

Revisions: 1

We show how to efficiently simulate the sending of a message M to a receiver who has partial information about the message, so that the expected number of bits communicated in the simulation is close to the amount of additional information that the message reveals to the receiver.

We ... more >>>


TR10-035 | 7th March 2010
Mark Braverman, Anup Rao, Ran Raz, Amir Yehudayoff

Pseudorandom Generators for Regular Branching Programs

We give new pseudorandom generators for \emph{regular} read-once branching programs of small width.
A branching program is regular if the in-degree of every vertex in it is (0 or) $2$.
For every width $d$ and length $n$,
our pseudorandom generator uses a seed of length $O((\log d + \log\log n ... 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 >>>


TR09-011 | 31st January 2009
Mark Braverman

Poly-logarithmic independence fools AC0 circuits

We prove that poly-sized AC0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has ... more >>>


TR07-035 | 3rd April 2007
Mark Braverman, Raghav Kulkarni, Sambuddha Roy

Parity Problems in Planar Graphs

We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2^k, for constant k. ... more >>>




ISSN 1433-8092 | Imprint