<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:st1="urn:schemas-microsoft-com:office:smarttags" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=us-ascii">
<meta name=Generator content="Microsoft Word 11 (filtered medium)">
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="PlaceType"/>
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="PlaceName"/>
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="place"/>
<!--[if !mso]>
<style>
st1\:*{behavior:url(#default#ieooui) }
</style>
<![endif]-->
<style>
<!--
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:purple;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:Arial;
color:windowtext;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;}
div.Section1
{page:Section1;}
-->
</style>
</head>
<body lang=EN-US link=blue vlink=purple>
<div class=Section1>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>When:
Thursday,
February 28, 2008 @ 10:00 am<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Where:
TTI-C Conference Room<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Who:
Jan Vondrak,
<st1:place w:st="on"><st1:PlaceName w:st="on">Princeton</st1:PlaceName> <st1:PlaceType
w:st="on">University</st1:PlaceType></st1:place><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Topic:
Approximation
algorithms for combinatorial allocation problems<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Combinatorial allocation problems arise in situations where
a set of items should be distributed among n players in order to maximize a
certain social utility function. Such problems have been subject to recent
interest due to their applications in combinatorial auctions and electronic
commerce. Since allocation problems are typically NP-hard to solve optimally,
we seek approximation algorithms that find a solution of value at least c * OPT
where OPT is the optimum and c<1 a suitable constant. I will discuss the
history of these problems and how they relate to classical work in
combinatorial optimization.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>A case of particular interest is the Submodular Welfare
Problem where utility functions are assumed to be monotone and submodular, a
property known in economics as "diminishing returns". It has been
known that a greedy algorithm yields a 1/2-approximation for this problem, and
more generally for the problem of submodular maximization subject to a matroid
constraint [Nemhauser, Wolsey, Fisher '78]. Among other results, I will show
how this can be improved to a (1-1/e)-approximation - an approximation factor
which is known to be optimal. A new ingredient in the algorithm is the
approximate solution of a non-linear optimization problem using a
"continuous greedy process".<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Contact:
Julia Chuzhoy,
TTI-C cjulia@tti-c.org
773-834-2490<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
</div>
</body>
</html>