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New York Area Theory Day
Organized by: IBM/NYU/Columbia
Friday, November 11, 2011
Courant Institute of Mathematical Sciences,
New York University, 251 Mercer Street, Auditorium 109, New York.
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.
Program:
Program
9:30 - 10:00 Coffee and bagels
10:00 - 10:55 Prof. Dana Ron
On sublinear algorithms for approximating
graph parameters
10:55 - 11:05 Short break
11:05 - 12:00 Dr. Mihai Pătraşcu
Hashing for Linear Probing
12:00 - 2:00 Lunch break
2:00 - 2:55 Prof. Oded Regev
Entropy-based Bounds on Dimension Reduction
in L_1
2:55 - 3:15 Coffee break
3:15 - 4:10 Prof. Benny Pinkas
Secure Computation on the Web:
Computing without Simultaneous Interaction
For directions, please see here and here (building 46)
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@watson.ibm.com
Baruch Schieber sbar@watson.ibm.com
Rocco Servedio rocco@cs.columbia.edu
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Abstracts
Prof. Dana Ron
(Tel-Aviv University and Columbia University)
On sublinear algorithms for approximating
graph parameters
When we refer to efficient algorithms, we usually mean
polynomial-time algorithms. In particular this is true for graph algorithms,
which are considered efficient if they run in time polynomial in the number
of vertices and edges of the graph.
However, in some cases we may seek even more efficient algorithms whose
running time is sublinear in the size of the input graph. Such algorithms
do not even read the whole input graph, but rather sample random parts
of the graph and compute approximations of various parameters of interest.
In this talk I will survey various such algorithms, where the parameters I
will discuss are:
(1) The average degree the number of small stars
(2) The weight of a minimum spanning tree
(3) The size of a minimum vertex cover and a maximum matching
(4) The number of edges that should be added/removed in order to
obtain various properties
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Dr. Mihai Pătraşcu
(AT&T Labs -- Research)
Hashing for Linear Probing
Hash tables are ubiquitous data structures solving the dictionary
problem, and they often show up in inner loops, making performance critical.
A hash table algorithm relies crucially on a hash function, which
quasirandomly maps a large domain (the input keys) to a small domain
(the memory space available). Many "hash tables" (in effect,
algorithms for dealing with collisions) have been proposed, the best
known being collision chaining, linear probing and cuckoo hashing.
Among these, linear probing is ideally suited for modern computer
architectures, which tend to favor linear scans. However, linear
probing is quite sensitive to the quality of the hash function and,
traditionally, good performance was only guaranteed by using highly
independent (but slow) hash functions.
Our finding is that tabulation hashing, despite its low degree of
independence, can actually guarantee very robust performance in linear
probing. This function is both easy to implement and extremely fast on
current hardware (faster than 2 multiplications), offering an ideal solution
both in theory and in practice.
==================================================================
Prof. Oded Regev
(Tel-Aviv University and CNRS, ENS, Paris)
Entropy-based Bounds on Dimension Reduction
in L_1
We show that there exists an N-point subset of L_1 such that for
every D>1, embedding it into \ell_1^d with distortion D requires
dimension d at least N^{\Omega(1/D^2)}, and that for every \eps>0
there exists an N-point subset of L_1 such that embedding it into
\ell_1^d with distortion 1+\eps requires dimension d at least
N^{1-O(1/\log(1/\eps))}. These results were previously proven by
Brinkman and Charikar [JACM, 2005] and by Andoni, Charikar, Neiman,
and Nguyen [FOCS 2011]. We provide an alternative and arguably more
intuitive proof based on an entropy argument.
==================================================================
Prof. Benny Pinkas
(Bar Ilan University and Google)
Secure Computation on the Web:
Computing without Simultaneous Interaction
Secure computation enables mutually suspicious parties to
compute a joint function of their private inputs while providing
strong security guarantees. However, its use in practice seems
limited. We argue that one of the reasons for this is that the model
of computation on the web is not suited to the type of communication
patterns needed for secure computation. Specifically, in most web
scenarios clients independently connect to servers, interact with them
and then leave. This rules out the use of secure computation protocols
that require that all participants interact simultaneously.
We initiate a study of secure computation in a client-server model
where each client connects to the server once and interacts with it,
without any other client necessarily being connected at the same time.
We point out some inherent limitations in this model and present
definitions that capture what can be done. We also present a general
feasibility result and several truly practical protocols for a number
of functions of interest. All our protocols are based on standard
assumptions, and we achieve security both in the semi-honest and
malicious adversary models.
Joint work with Shai Halevi and Yehuda Lindell.
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