The IBM Research/NYU/Columbia Theory Day
Friday, November 19, 2004
Room 109 Warren Weaver Hall
251 Mercer Street
New York, NY 100121185
Program
9:30  10:00 Coffee and bagels
10:00  10:55 Prof. Sampath Kannan
Algorithms for Streamed Graphs and Streaming Lower Bounds
10:55  11:05 Short Break
11:05  12:00 Prof. Sanjeev Arora
Geometric Embeddings, Graph Partitioning, and Expander Flows: A survey of recent results
12:00  2:00 Lunch break
2:00  2:55 Prof. Silvio Micali
Collusion Free Protocols
2:55  3:15 Coffee break
3:15  4:10 Prof. Joan Feigenbaum
Progress on the PORTIA Project
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Organizers:
Yevgeniy Dodis dodis@cs.nyu.edu
TalRabin talr@watson.ibm.com
Baruch Shieber talr@watson.ibm.com
Rocco Servedio rocco@cs.columbia.edu
Abstracts
Algorithms and Lower Bounds for Streamed Graphs
Prof. Sampath Kannan
University of Pennsylvania
The streaming model of computation is relevant to situations where the
amount of input data far exceeds the storage capacity of the computer. The
model typically assumes that the space available is polylogarithmic in the
size of the input and that the input is streamed in a read once fashion.
In this talk we consider the situation where the input is a graph with n
vertices and m edges, whose edges are streamed (in adversarial order).
After arguing that o(n) space is insufficient even for the ``simplest''
tasks, we focus on what can be done with space O(n polylog n). Here too
the news is not very good when we restrict our attention to onepass
algorithms. After showing some one pass algorithms for approximating the
distance, approximating the size and weight of matchings etc., we turn our
attention to multipass algorithms. We show passspace tradeoffs for
matching and lower bounds for a pointerchasinglike problem.
(joint work with Joan Feigenbaum, Andrew McGregor, Siddharth Suri, Jian
Zhang)
Geometric Embeddings, Graph Partitioning, and Expander Flows:
A survey of recent results
Prof. Sanjeev Arora
Princeton University
Partitioning a graph into two (or more) large pieces while minimizing the
size of the ``interface'' between them is a fundamental combinatorial
problem. Graph partitions or separators are central objects of study in
the theory of Markov chains, geometric embeddings and are a natural
algorithmic primitive in numerous settings, including clustering, divide
and conquer approaches, PRAM emulation, VLSI layout, and packet routing in
distributed networks. Most versions of graph partitioning are NPhard, so
researchers have tried to develop approximation algorithms.
The past year has seen a flurry of new approximation algorithms, starting
with a paper of mine with Satish Rao and Umesh Vazirani in STOC'04 that
gave a \sqrt{log n}approximation for SPARSEST CUT. This improved
classical algorithms based upon both spectral methods and multicommodity
flows (Leighton Rao 1988; O(log n)approximation). We also introduced the
notion of expander flows, which constitute an interesting ``certificate''
of a graph's expansion.
The [ARV] algorithm used semidefinite programming and hence was not too
efficient. In joint work with Hazan and Kale (FOCS'04) we give a more
combinatorial algorithm. It runs in nearquadratic time, raising hopes of
practical impact.
Finally, the ideas used in the [ARV] approximation algorithm have led to
sudden progress in another research area: lowdistortion embeddings of
finite metric spaces into geometric spaces (such as l_2). Recent
unpublished papers (Chawla, Gupta, Racke; improved upon in my joint work
with Lee and Naor) show how to embed npoint subsets of l_1 into l_2 with
distortion much better than Bourgain's bound of O(log n) from 1985. Thus
algorithmic ideas have helped resolve questions in pure mathematics.
The talk will be a selfcontained survey of the above results, as well as
several papers not mentioned above.
Collusion Free Protocols
Prof. Silvio Micali
MIT
Secure computation does not prevent a set of bad players from sharing
information and coordinating their actions during a protocol. But not
even two colluding players should be tolerated in say Mental Poker.
We define CollusionFree Protocols, and construct them (under standard
physical and computational assumptions) for Poker, Bridge and all similar
games.
A key step of our solution is making steganography provably impossible.
Joint work with Matt Lepinski and Abhi Shelat
Progress on the PORTIA Project
Prof. Joan Feigenbaum
Yale University
Increasing use of computers and networks in business, government,
recreation, and almost all aspects of daily life has led to a
proliferation of online sensitive data, i.e., data that, if used
improperly, can harm the data subjects, data owners, data users, or other
relevant parties. As a result, concern about the ownership, control,
privacy, and accuracy of these data has become a top priority. PORTIA
(http://crypto.stanford.edu/portia/) is a largeITR project focused on
both the technical challenges of handling sensitive data and the policy
and legal issues facing data subjects, data owners, and data users. The
project has been in operation since Oct 2003. This talk, suitable both
for a Computer Science audience and for a "Society and Technology"
audience, will survey some of the progress and some of the remaining open
questions in the PORTIA project.
http://www.cs.yale.edu/homes/jf
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