
Friday April 9 
10.00A.M. 
Coffee 
10.20A.M. 
Guy Blelloch, Carnegie
Mellon
Welcome and Introductions 
10.30A.M. 
Michael
Kearns, University of Pennsylvania
The Economics of Social Networks
In an attempt to explain a number of apparently universal
statistical properties of natural social and economic networks,
many authors have proposed rich families of probabilistic
generative models for social network formation. We have
recently introduced a graphtheoretic representation for
classical mathematical economic models. This work studies
the marriage of these two lines of inquiry: we examine the
network effects that social network models (such as preferential
attachment) introduce into classical economic settings.
Of particular interest are the relationships between the
statistical structure of the network, and economic metrics
such as wealth distribution and price variation. Our findings
are a mixture of theoretical results and largescale simulations
that have been made possible only by algorithmic advances
of the last two years.
Joint work with Sham Kakade, Luis Ortiz, Robin
Pemantle, and Sid Suri. 
11.30A.M. 
Milena
Mihail, Georgia Tech
Conductance of Power Law and Scale
Free Graphs
Abstract: We generalize the
classical result of expansion of random regular graphs for
graphs whose degree sequences follow heavy tailed statistics.
Such graphs arise in complex networks like the Internet,
the WWW and biological networks. In particular, we establish
constant conductance in the configurational random graph
model known as power law random graph, and in the evolutionary
model of growth with preferential attachment, under the
assumption that the minimum degree is at least three. As
an immediate consequence, we get separation of 1st and 2nd
eigenvalues of the stochastic normalization of the adjacency
matrix of the graph, with many further algorithmic implications,
as well as many open problems, in the corresponding application
areas. 
12.30P.M. 
Lunch 
2.00P.M. 
Lincoln
Lu, UC San Diego
Spectra of random power law graphs
(pdf1),
(pdf2),
(pdf3)
Abstract: In the study of
the spectra of power law graphs, there are basically two
competing approaches. One is to prove analogues of Wigner's
semicircle law while the other predicts that the eigenvalues
follow a power law distributions. Although the semicircle
law and the power law have nothing in common, we will show
that both approaches are essentially correct if one considers
the appropriate matrices. We will prove that (under certain
mild conditions) the eigenvalues of the (normalized) Laplacian
of a random power law graph follow the semicircle law while
the spectrum of the adjacency matrix of a power law graph
obeys the power law. Our results are based on the analysis
of random graphs with given expected degrees and their relations
to several key invariants. Of interest are a number of (new)
values for the exponent $\beta$ where phase transitions
for eigenvalue distributions occur. The spectrum distributions
have direct implications to numerous graph algorithms such
as randomized algorithms that involve rapidly mixing Markov
chains, for example.
This is a joint work with Lincoln Lu, Fan Chung,
and Van Vu. 
3.00P.M. 
Sanjeev
Arora, Princeton University
Expander flows and a sqrt{log n}approximation
for graph expansion/sparsest cut
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.
Classical algorithms for these problems include eigenvalue
approaches (Cheeger 1970, Alon 1985) and multicommodity
flows (Leighton and Rao 1988). The latter yields a O(log
n)approximation, and it has been an open problem to improve
this ratio. We describe a new O(\sqrt{log n})approximation
algorithm.
The algorithm relies on semidefinite relaxations that use
the triangle inequality constraints. Analysing these relaxations
had been an important open problem as well.
We also introduce the notion of {\em expander flows}, which
constitute an interesting ``certificate'' of a graph's expansion.
We use them to prove a surprising new theorem about graph
embeddings: for every nnode graph it is possible to embed
an nnode expander graph in it with appropriate dilation
and congestion. We think this embedding theorem may have
other applications.
Our techniques are an interesting mix of graph theory and
highdimensional geometry, including the use of "measure
concentration." The talk will be selfcontained, and
showcases a newer proof that is simpler than the one in
earlier versions of the paper.
(Joint work with Satish Rao and Umesh Vazirani;
to appear at ACM STOC 2004)

4.00P.M. 
Coffee 
4.30P.M. 
Andrei
Broder, IBM Research
Sic Transit Gloria Telae: Towards
an Understanding of the Webs Decay (pdf)
Abstract: The rapid growth
of the World Wide Web has been noted, tracked, and modeled
extensively. However, recent studies have documented
the dual phenomenon: web pages have short half lives, and
thus the Web exhibits rapid death as well. Consequently,
page creators are faced with an increasingly difficult task
of keeping links and content uptodate: many pages are
seldom updated, becoming ``decayed'', and less effective
as information resources.
In this work we formalize a page ``decay'' measure based
solely on the Web graph properties and present algorithms
for computing it efficiently. We explore this measure
by presenting a number of validations, and use it to identify
interesting artifacts on today's Web. We then describe
a number of potential applications of interest to search
engines, web page maintainers, ontologists, and individual
users.
There are many open questions: Can this measure be made
more accurate by combining it with NLP page content analysis?
Can we make decay inferences from observed page changes
over a long time period? What is a good birth/death
model for the Web graph that agrees with our empirical observations?
Time permitting we will explore these and more.
This is joint work with Ziv BarYossef, Ravi
Kumar, and Andrew Tomkins. 
7.00P.M. 
Workshop Dinner 

Saturday April 10 
8.45A.M. 
Coffee 
9.15P.M. 
Andrew
Tomkins, IBM Almaden
Online Conversations: Aliases,
Topics, and Propagation Networks (pdf1),
(pdf2)
Abstract: In this talk, we
consider three aspects of online conversations across the
web, as seen in bulletin boards, blogs, and communities.
First, we consider the viability of pseudonyms, or aliases,
as a mechanism to allow users to participate anonymously
in these conversations. We show algorithms that are disturbingly
effective at linking together the multiple aliases of a
single author through analysis of the message content. Next,
we consider the structure of the topics that emerge in online
conversations, and present a recursive formulation of conversation
structure based on an experimental study. Finally, we present
a simple model for the flow of a topic from one user to
another based on the theory of infectious diseases, and
we present a simple iterative algorithm to learn such models
from observations of conversations.
Variously joint work with R. Guha, Daniel Gruhl,
David LibenNowell, Jasmine Novak, and Prabhakar Raghavan.

10.15A.M. 
Coffee 
10.30A.M. 
Fan
Chung Graham
Coupling online and offline analyses
for random power law graphs
Abstract: We develop a coupling
technique for analyzing online models by using offline
models. This method is especially effective for a growthdeletion
model which generalizes and includes the preferential attachment
model for generating large complex networks that simulate
numerous realistic networks. The analysis has made use of
two tools  a general framework for comparing different
random graph models and a general Martigale inequality that
requires only a weak Lipschitz condition. By coupling the
online model with the offline model for random power law
graphs, we derive bounds for a number of graph properties
including diameter, average distances, connected components
and spectral bounds. For example, we prove that a power
law graph generated by the growthdeletion model almost
surely has diameter $ O(\log n)$ and average distance $
O(\log \log n)$.
This is a joint work with Lincoln Lu 
11.30A.M. 
Peter
Dodds, Columbia University
Social Search and the Small World
Phenomenon: Experiment and Theory
(pdf1),
(pdf2),
(pdf3,)
(pdf4)
Abstract: Social networks
have the surprising property of being ``searchable'': ordinary
people are capable of directing messages through their network
of contacts to reach a specific but distant target person
in relatively few steps (<10). This property of searchability
is popularly embraced as the notion that the world is `small'
and was first studied experimentally by Stanley Milgram
in the late 1960's. I will present results from an online
version of Milgram's experiment along with a theoretical
model that offers an explanation of social network searchability
in terms of recognizable personal identities defined along
a number of social dimensions. Our model defines a class
of searchable networks and a method for searching them that
may be applicable to many network search problems including
the location of data files in peertopeer networks, pages
on the World Wide Web, and information in distributed databases. 
12.30P.M. 
Lunch 
1.30P.M. 
Pedro
Domingos, University of Washington
Modeling and optimizing word of mouth
(pdf1),
(pdf2)
Abstract: Viral marketing
exploits word of mouth in online networks. When successful,
it can produce massive returns from minimal investment.
Unfortunately, success is very hard to ensure. Our research
seeks to make viral marketing less of a black art and more
of a quantitative process. We model social networks as Markov
random fields, and mine these networks from data. We define
the network value of a customer to be the expected gain
in profits from other customers that results from marketing
to her. We then identify the set of nodes with (ideally)
maximal network value, market to them, and unleash a wave
of word of mouth. Experiments on the Epinions Web of Trust
and other networks demonstrate the benefits of this approach,
its robustness to incomplete information, and the extremely
high network value of some customers.
Time permitting, I will also briefly survey other Web research
at the University of Washington, including predicting the
evolution of the Web, combining link and content information
in Web search, propagating trust across networks, and modeling
the behavior of Web surfers.
Joint work with Matt Richardson. 
2.30P.M. 
David
Kempe
Maximizing the Spread of Influence
in a Social Network (pdf)
Abstract: A social network
 the graph of relationships and interactions within a group
of individuals  plays a fundamental role as a medium for
the spread of information, ideas, and influence among its
members. An idea or innovation will appear  for example,
the use of cell phones among college students, the adoption
of a new drug within the medical profession, or the rise
of a political movement in an unstable society  and it
can either die out quickly or make significant inroads into
the population.
The resulting collective behavior of individuals in a social
network has a long history of study in sociology. Recently,
motivated by applications to wordofmouth marketing, Domingos
and Richardson proposed the following optimization problem:
allocate a given "advertising" budget so as to
maximize the (expected) number of individuals who will have
adopted a given product or behavior.
In this talk, we will investigate this question under the
mathematical models of influence studied by sociologists.
We present and analyze a simple approximation algorithm,
and show that it guarantees to reach at least a 11/e (roughly
63%) fraction of what the optimal solution can achieve,
under many quite general models. In addition, we experimentally
validate our algorithm, comparing it to several widely used
heuristics on a data set consisting of collaborations among
scientists.
Joint work with Jon Kleinberg and Eva Tardos 
3.30P.M. 
Coffee 
4.00P.M. 
Marcio
Menezes, University of Notre Dame
Hot Spots and Universality in Network
Dynamics
Most complex networks serve as conduits for various dynamical
processes, ranging from mass transfer by chemical reactions
in the cell to packet transfer on the Internet. We collected
data on the time dependent activity of various natural and
technological networks, finding evidence of orders of magnitude
differences in the fluxes of individual nodes. This dynamical
inhomogeneity reflects the emergence of localized high flux
regions or ``hot spots'', carrying an overwhelming fraction
of the network's activity. We also find that each system
is characterized by a unique scaling law, coupling the flux
fluctuations with the total flux on individual nodes, a
result of the competition between the system's internal
collective dynamics and changes in the external environment
[M. Argollo de Menezes and A.L. Barabasi, Phys. Rev. Lett.
92, 028701 (2004)]. We propose a method to separate these
two components, allowing us to predict the relevant scaling
exponents and correlate them to the susceptibility of different
systems to perturbations. As multichannel measurements are
becoming the norm in most fields, the method could help
uncover the collective dynamics of a wide array of complex
systems.
Joint with A.L. Barabasi. 
Web Structure and Algorithms Workshop
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