[Colloquium] DATE CHANGE: Julia Chuzhoy Talk on May 4, 2009

[Katie Casey]

DEPARTMENT OF COMPUTER SCIENCE

UNIVERSITY OF CHICAGO

Date: Monday, May 4, 2009
Time: 3:45 p.m.
Place: RY 251

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Speaker:	Julia Chuzhoy

From:		Toyota Technical Institute - Chicago

Website: 	 http://www.cs.uchicago.edu/people/cjulia

Title:     Allocating Goods to Maximize Fairness

Abstract:     We consider the Max-Min Allocation problem, in which we
are given a set of m agents and a set of n items, together with
utilities u(A,i) of agent A for item i. Our goal is to allocate items
to agents to maximize fairness. Specifically, the utility of an agent
is the sum of its utilities for items it receives, and we seek to
maximize the minimum utility of any agent. While this problem has
received much attention recently, its approximability has not been
well-understood thus far: the best known approximation algorithm
achieves a roughly O(\sqrt m)-approximation,  and in contrast, the
best known hardness of approximation stands at $2$. Our main result is
an approximation algorithm that achieves a $\tilde{O}(n^{\eps})$
approximation in time $n^{O(1/\eps)}$, for any $\eps=\Omega(\log\log n/
\log n)$.  In particular, we obtain poly-logarithmic approximation in
quasi-polynomial time, and for every constant $\eps > 0$, we obtain an
$O(n^{\eps})$-approximation in polynomial time. An interesting
technical aspect of our algorithm is that we use as a building block a
linear program whose integrality gap is $\Omega(\sqrt m)$. We bypass
this obstacle by iteratively using the solutions produced by the LP to
construct new instances with significantly smaller integrality gaps,
eventually obtaining the desired approximation. Joint work with
Deeparnab Chakrabarty and Sanjeev Khanna


Refreshments will be served prior to the talk in RY 255.
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