Geometry and Expansion: A Survey of Recent Results
Sanjeev Arora
Princeton University
Thursday, November 9, 2006
9:30 a.m. in 2310 CS
(refreshments at 9:00)
Abstract:
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.
This talk surveys a new geometric view of expansion that has led to new
results in computer science and mathematics. It originated in some joint
work with Satish Rao and Umesh Vazirani and has motivated several other
papers. It has led to better approximation algorithms for a host of
NP-hard combinatorial problems (including SPARSEST CUT, MIN-2-CNF
DELETION, MIN-LINEAR ARRANGEMENT). It has also led to better geometric
embeddings for metric spaces, including a proof that every n-point l_1
space embeds in l_2 with distortion close to O(\sqrt{log n}), improving
upon the trivial O(log n) bound from Bourgain's theorem.
Other applications include a better structural understanding of graph
expansion, as well as faster algorithms for approximating expansion.
Speaker's Bio:
Sanjeev Arora is Professor of Computer Science at Princeton University
and works in computational complexity theory, approximation algorithms
for NP-hard problems, geometric algorithms, and probabilistic algorithms.
He has received the ACM Dissertation Prize, the SIGACT-EATCS Goedel
Prize, and the Packard Fellowship.
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