Difference between revisions of "CATS-Mar-15-2013"

From Theory
 
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== Title ==
 
== Title ==
Revisiting the Ranking Algorithm for Greedy Randomized Matching on Arbitrary Graphs
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The Degree of Segregation in Social Networks
  
 
== Speaker ==
 
== Speaker ==
Hubert ChanDepartment of Computer Science, The University of Hong Kong
+
Nicole ImmorlicaMicrosoft Research
  
 
== Abstract ==
 
== Abstract ==
Motivated by online advertisement and exchange settings, greedy
+
In 1969, economist Thomas Schelling introduced a landmark model of racial segregation in which individuals move out of neighborhoods where their ethnicity constitutes a minority. Simple simulations of Schelling's model suggest that this local behavior can cause global segregation effects. In this talk, we provide a rigorous analysis of Schelling's model on ring networks. Our results show that, in contrast to prior interpretations, the outcome is nearly integrated: the average size of an ethnically-homogenous region is independent of the size of the society and only polynomial in the size of a neighborhood.  
randomized algorithms for the maximum matching problem have been
 
studied, in which the algorithm makes (random) decisions that are
 
essentially oblivious to the input graph. Any greedy algorithm can
 
achieve performance ratio 0.5, which is the expected number of matched
 
nodes to the number of nodes in a maximum matching.
 
Since Aronson, Dyer, Frieze and Suen proved that the Modified
 
Randomized Greedy (MRG) algorithm achieves performance ratio 0.5000025
 
on arbitrary graphs in the mid-nineties, no further attempts in the
 
literature have been made to improve this theoretical ratio for
 
arbitrary graphs until two papers were published in FOCS 2012.
 
  
In this talk, we revisit the Ranking algorithm using the LP framework.
+
Joint work with Christina Brandt, Gautam Kamath, and Robert D. Kleinberg.
Special care is given to analyze the structural properties of the
 
Ranking algorithm in order to derive the LP constraints, of which one
 
known as the boundary constraint requires totally new analysis and is
 
crucial to the success of our LP. We use continuous LP relaxation to
 
analyze the limiting behavior as the finite LP grows. Of particular
 
interest are new duality and complementary slackness characterizations
 
that can handle the monotone and the boundary constraints in
 
continuous LP. We believe our work achieves the currently best
 
theoretical performance ratio of 0.523 on arbitrary graphs.
 

Latest revision as of 15:08, 18 July 2013

Title[edit]

The Degree of Segregation in Social Networks

Speaker[edit]

Nicole Immorlica, Microsoft Research

Abstract[edit]

In 1969, economist Thomas Schelling introduced a landmark model of racial segregation in which individuals move out of neighborhoods where their ethnicity constitutes a minority. Simple simulations of Schelling's model suggest that this local behavior can cause global segregation effects. In this talk, we provide a rigorous analysis of Schelling's model on ring networks. Our results show that, in contrast to prior interpretations, the outcome is nearly integrated: the average size of an ethnically-homogenous region is independent of the size of the society and only polynomial in the size of a neighborhood.

Joint work with Christina Brandt, Gautam Kamath, and Robert D. Kleinberg.