Extremal Graph Theory
Extremal Graph Theory
Finding structures in large-scale graphs
One of the most dramatic advantages afforded by recent advances in internet technology and sensing technology is the ability to persistently survey one or several domain(s) in land, air, sea, space and
even cyber space, resulting in a preponderance of all sorts of information, which can then be accessed
almost instantly across the globe via the internet. However, this enrichment of data comes at a
cost. First of all, the sheer volume currently overwhelms even the best algorithms and systems
that had been developed to process these types of data. Furthermore, not all of these data are
good or equally important - some data are raw in the sense that there are much uncertainty and
misalignment in them; and other data are just redundant and/or can be considered as noise that
obfuscate the massive data rending them not well understood. In this information age that we
live in, there is, therefore, a growing need to respond to the challenges to make sense of all these
data, often modeled by large-scale graphs that represent various communication networks, sensor
networks, social networks, etc.
In response to such challenges, we herein propose a framework using advanced tools from random graph theory and spectral graph theory by which to carry out the quantitative
analysis of the structure and dynamics of large networks..... More coming...
Sunday, January 26, 2014