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Electronic Colloquium on Computational Complexity

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All reports by Author Anup Rao:

TR17-040 | 4th March 2017
Sivaramakrishnan Natarajan Ramamoorthy, Anup Rao

Non-Adaptive Data Structure Lower Bounds for Median and Predecessor Search from Sunflowers

Revisions: 2

We prove new cell-probe lower bounds for data structures that maintain a subset of $\{1,2,...,n\}$, and compute the median of the set. The data structure is said to handle insertions non-adaptively if the locations of memory accessed depend only on the element being inserted, and not on the contents of ... more >>>

TR14-060 | 21st April 2014
Anup Rao, Amir Yehudayoff

Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness

Revisions: 1

We show that the deterministic multiparty communication complexity of set disjointness for $k$ parties on a universe of size $n$ is $\Omega(n/4^k)$. We also simplify Sherstov's proof
showing an $\Omega(\sqrt{n}/(k2^k))$ lower bound for the randomized communication complexity of set disjointness.

more >>>

TR14-020 | 18th February 2014
Pavel Hrubes, Anup Rao

Circuits with Medium Fan-In

Revisions: 1

We consider boolean circuits in which every gate may compute an arbitrary boolean function of $k$ other gates, for a parameter $k$. We give an explicit function $f:\bits^n \rightarrow \bits$ that requires at least $\Omega(\log^2 n)$ non-input gates when $k = 2n/3$. When the circuit is restricted to being depth ... 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 >>>

TR12-143 | 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 >>>

TR11-160 | 1st December 2011
Zeev Dvir, Anup Rao, Avi Wigderson, Amir Yehudayoff

Restriction Access

We introduce a notion of non-black-box access to computational devices (such as circuits, formulas, decision trees, and so forth) that we call \emph{restriction access}. Restrictions are partial assignments to input variables. Each restriction simplifies the device, and yields a new device for the restricted function on the unassigned variables. On ... 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


We show that:

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

TR08-015 | 23rd January 2008
Anup Rao

Extractors for Low-Weight Affine Sources

We give polynomial time computable extractors for low-weight affine sources. A distribution is affine if it samples a random point from some unknown low dimensional subspace of F^n_2 . A distribution is low weight affine if the corresponding linear space has a basis of low-weight vectors. Low-weight ane sources are ... more >>>

TR08-013 | 16th January 2008
Anup Rao

Parallel Repetition in Projection Games and a Concentration Bound

In a two player game, a referee asks two cooperating players (who are
not allowed to communicate) questions sampled from some distribution
and decides whether they win or not based on some predicate of the
questions and their answers. The parallel repetition of the game is
the game in which ... more >>>

TR07-034 | 29th March 2007
Anup Rao

An Exposition of Bourgain's 2-Source Extractor

A construction of Bourgain gave the first 2-source
extractor to break the min-entropy rate 1/2 barrier. In this note,
we write an exposition of his result, giving a high level way to view
his extractor construction.

We also include a proof of a generalization of Vazirani's XOR lemma
that seems ... more >>>

TR05-106 | 26th September 2005
Anup Rao

Extractors for a Constant Number of Polynomial Min-Entropy Independent Sources

Revisions: 1

We consider the problem of bit extraction from independent sources. We
construct an extractor that can extract from a constant number of
independent sources of length $n$, each of which have min-entropy
$n^\gamma$ for an arbitrarily small constant $\gamma > 0$. Our
constructions are different from recent extractor constructions
more >>>

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