Computer Science Colloquium

New York Area Theory Day

IBM/NYU/Columbia,

Speaker Website

May 04, 2012 9:30AM
Schapiro (CEPSR) building, 412
Columbia University
New York, NY

Spring 2012 Colloquia Calendar

Host

Columbia University, New York
External sponsorship by: Google

Synopsis

The New York Area Theory Day is a semi-annual conference, aimed to bring together people in the New York Metropolitan area for one day of interaction and discussion. The Theory Day features several (usually 4-5) hour-long presentations by leading theoretical computer scientists about state-of-the-art advances in various areas. Some presentations give a survey of the latest advances in some area, while others may concentrate on a particular result.
The meeting is free and open to everyone; in particular, students are encouraged to attend.

For directions, please go to:
http://www.cs.columbia.edu/theory/directions.html

Program

9:30 - 10:00 Coffee and bagels

10:00 - 10:55 Prof. Michael Kearns (U Penn)
Experiments in Social Computation

10:55 - 11:05 Short break

11:05 - 12:00 Prof. Eli Ben-Sasson (Technion and Microsoft Research New England)
An Additive Combinatorics Approach Relating Rank to Communication Complexity

12:00 - 2:00 Lunch break

2:00 - 2:55 Dr. Aleksander Madry (Microsoft Research New England)
Online Algorithms and the K-server Conjecture

2:55 - 3:15 Coffee break

3:15 - 4:10 Dr. Shubhangi Saraf (IAS)
The Method of Multiplicities


To subscribe to our mailing list, follow instructions at
http://www.cs.nyu.edu/mailman/listinfo/theory-ny

Organizers:
Yevgeniy Dodis dodis@cs.nyu.edu
Tal Rabin talr@us.ibm.com
Baruch Schieber sbar@us.ibm.com
Rocco Servedio rocco@cs.columbia.edu


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ABSTRACTS

Experiments in Social Computation

Michael Kearns
University of Pennsylvania

What does the theory of computation have to say about the emerging
phenomena of crowdsourcing
and social computing? Most successful applications of crowdsourcing to
date have been on problems
we might consider "embarrassingly parallelizable" from a computational
perspective. But the power
of the social computation approach is already evident, and the road
cleared for applying it to more
challenging problems.

In part towards this goal, for a number of years we have been
conducting controlled human-subject
experiments in distributed social computation in networks with only
limited and local communication.
These experiments cast a number of traditional computational problems
--- including graph coloring,
consensus, independent set, market equilibria, and voting --- as games
of strategic interaction in
which subjects have financial incentives to collectively "compute"
global solutions. I will overview
and summarize the many behavioral findings from this line of
experimentation, and draw broad
comparisons to some of the predictions made by the theory of
computation and microeconomics.

==================================================================

An Additive Combinatorics Approach Relating Rank to Communication Complexity


Eli Ben-Sasson
Technion and Microsoft Research New England

For a {0,1}-valued matrix M let CC(M) denote the deterministic
communication complexity of the boolean function associated with M. It
is well-known since the work of Mehlhorn and Schmidt [STOC 1982] that
CC(M) is bounded from above by rank(M) and from below by log rank(M)
where rank(M) denotes the rank of M over the field of real numbers.
Determining where in this range lies the true worst-case value of
CC(M) is a fundamental open problem in communication complexity. The
state of the art is

log^{1.631} rank(M) < CC(M) < 0.415 rank(M),

the lower bound is by Kushilevitz [unpublished, 1995] and the upper
bound is due to Kotlov [Journal of Graph Theory, 1996]. Lovasz and
Saks [FOCS 1988] conjecture that CC(M) is closer to the lower bound,
i.e., CC(M) < log^c(rank(M)) for some absolute constant c --- this is
the famous ``log-rank conjecture'' --- but so far there has been no
evidence to support it, even giving a slightly non-trivial
(o(rank(M))) upper bound on the communication complexity.

Our main result is that, assuming the Polynomial Freiman-Ruzsa (PFR)
conjecture in additive combinatorics, there exists a universal
constant c such that

CC(M)< c rank(M)/ log rank(M).

Although our bound is stated using the rank of M over the reals, our
proof goes by studying the problem over the finite field of size 2,
and there we bring to bear a number of new tools from additive
combinatorics which we hope will facilitate further progress on this
perplexing question.

In more detail, our proof is based on the study of the ``approximate
duality conjecture'' which was suggested by Ben-Sasson and Zewi [STOC
2011] and studied there in connection to the PFR conjecture. First we
improve the bounds on approximate duality assuming the PFR conjecture.
Then we use the approximate duality conjecture (with improved bounds)
to get our upper bound on the communication complexity of low-rank
martices.

Joint work with Shachar Lovett (IAS) and Noga Ron-Zewi (Technion)


==================================================================

Online Algorithms and the K-server Conjecture

Aleksander Madry
Microsoft Research New England

Traditionally, in the problems considered in optimization, one
produces the solution only after the whole input is made available.
However, in many real-world scenarios the input is revealed gradually,
and one needs to make irrevocable decisions along the way while having
only partial information on the whole input. This motivates us to
develop models that allow us to address such scenarios.

In this talk, I will consider one of the most popular approaches to
dealing with uncertainty in optimization: the online model and
competitive analysis; and focus on a central problem in this area: the
k-server problem. This problem captures many online scenarios - in
particular, the widely studied caching problem - and is considered by
many to be the "holy grail" problem of the field.

I will present a new randomized algorithm for the k-server problem
that is the first online algorithm for this problem that achieves
polylogarithmic competitiveness.

Based on joint work with Nikhil Bansal, Niv Buchbinder, and Joseph (Seffi) Naor.

==================================================================

The Method of Multiplicities

Shubhangi Saraf
IAS

Polynomials have played a fundamental role in the construction of objects with
interesting combinatorial properties, such as error correcting codes,
pseudorandom generators, randomness extractors etc. Somewhat strikingly,
polynomials have also been found to be a powerful tool in the analysis of
combinatorial parameters of objects that have some algebraic structure. This
method of analysis has found applications in works on list-decoding of error
correcting codes, constructions of randomness extractors, and in obtaining
strong bounds for the size of Kakeya Sets. Remarkably, all these applications
have relied on very simple and elementary properties of polynomials
such as the sparsity of the zero sets of low degree polynomials.

In this talk we will discuss improvements on several of the results mentioned
above by a more powerful application of polynomials that takes into
account the information contained in the *derivatives* of the
polynomials. We call this
technique the ``method of multiplicities". The information about higher
multiplicity vanishings of polynomials, which is encoded in the derivative
polynomials, enables us to meaningfully reason about the zero sets of
polynomials of degree much higher than the underlying field size.

We will discuss some of these applications of the method of multiplicities, to
obtain improved constructions of error correcting codes, and qualitatively
tighter analyses of Kakeya sets, and randomness extractors.

(Based on joint works with Zeev Dvir, Swastik Kopparty, Madhu Sudan, Sergey
Yekhanin)


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