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Prof. Sebastian Cioaba has been awarded a
Young Investigator grant from the National Security Agency, for his
project entitled "Problems in Algebraic and Extremal Graph Theory".
Graph theory is the main tool for
investigating large information networks including the web graph, social
or biological networks and is useful in many applications such as
network design, web-page ranking or routing network trac. The size of
such networks is often very large (ranging from hundreds of thousands to
billions of nodes) and analyzing their structure by brute force is not
feasible. The challenge is to use a small number of parameters who
capture the shape of the network. Spectral graph theory (the study of
eigenvalues of graphs) provides important algebraic tools for studying
structural properties of graphs and has connections to other areas such
as expander graphs, computer science, ranking, network design and
error-correcting codes. Eigenvalue interlacing gives information about
substructures in networks. In this project, Prof. Cioaba is using
algebraic, combinatorial and geometric techniques to investigate the
structure of minimum (non-local) disconnecting sets of nodes in
networks, to determine the expansion properties of graphs constructed
from certain linear systems of equations and to study the decomposition
of (hyper)graphs into minimum number of cuts or bicliques.
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