[talks] A Vijayaraghavan preFPO
Melissa M. Lawson
mml at CS.Princeton.EDU
Thu Mar 1 14:32:14 EST 2012
Aravindan Vijayaraghavan will present his preFPO on
Wednesday March 7 at 11AM in Room 302 (note room). The
members of his committee are: Moses Charikar, advisor;
Sanjeev Arora and Mark Braverman, readers; David Blei
and Konstantin Makarychev, nonreaders. Everyone is invited
to attend his talk. His abstract follows below.
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Understanding Approximability through Average-case Analysis
We study the approximability of fundamental graph optimization problems through
approximation algorithms for both realistic average-case and
worst-case instances of problems.
We study average-case instances to shed new light on approximability
in two ways :
1. designing better algorithms for realistic average-case instances.
2. designing new algorithms with better guarantees even in worst-case, and
identifying new barriers for further progress.
In the first part of the thesis, we study Graph partitioning problems
which are ubiquitous in computer science and form a central topic of
study. However, constant factor approximations have been elusive.
Since real-world instances are unlikely to behave like worst-case
instances, a compelling question is :
can we design better algorithms for realistic average case instances?
We study a semi-random model for graph partitioning problems, that is
more general than previously studied random models, and that seems to
capture many real-world instances well. We design new O(1) approximation
algorithms for classical graph partitioning problems like Balanced Separator,
Sparsest cut, Multicut and Small set expansion for these semi-random
instances. Our algorithms are based on new SDP-based techniques and
work in a wider range of parameters than algorithms for previously
studied random and semi-random models.
In the second part, we show how insights from algorithms for a natural
average-case version are used to obtain new worst-case approximation
algorithms for the Densest k-Subgraph problem -- an important yet poorly
understood problem in combinatorial optimization. The counting-based algorithms
for the average-case version of the problem are translated to algorithms for
the worst-case using linear programming hierarchies: this gives
an improved n^{1/4} factor approximation. Studying the average-case
version also points to a concrete barrier for further progress on
approximations for Densest k-subgraph.
These results are based on joint works with Aditya Bhaskara, Moses
Charikar, Eden Chlamtac, Uriel Feige, Venkatesan Guruswami, Konstantin
Makarychev, Yury Makarychev and Yuan Zhou.
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