**UT Arlington Faculty:** Bill Corley, Jay Rosenberger

**Collaborators:** Eli Olinick

**Topics:** Small world networks, Scale-free networks, Network optimization, Network complexity theory, Telecommunications

**Description:** Information, money, and disease
are disseminated through systems arising both in nature and our
technical society. Such systems are modeled by graphs in which objects
of interest are represented by vertices connected by edges. In such
systems, the notion of connectivity is perhaps the most important
property, and a variety of fields, from quantum physics to disease
epidemiology, display a similar underlying structure. Highly connected
networks are called small-world networks. Diverse examples of such
small-world networks with these properties include the World Wide Web as
a network of websites, the brain as a network of neurons, and an
organization as a network of people. To design networks, modelers will
determine appropriate vertices and edges to represent the system and
then employ network optimization techniques to develop an optimal
design. COSMOS has studied small-world and scale-free networks, measures
of a network’s complexity and connectivity, and telecommunications
networks.

- Olinick, E. V. and J. M. Rosenberger (2008). “Optimizing revenue in CDMA networks under demand uncertainty.”
*European Journal of Operational Research*,**186(2)**, pp. 812–825. - Rosenberger, J. M. and E. V. Olinick (2007). “Robust Tower Location for CDMA Networks”
*Naval Research Logistics*,**54**, pp. 151–161. - Rosenberger, J. M. and H. W. Corley (2005). “Mathematical Programming Models for Some Smallest World Problems.”
*Nonlinear Analysis: Real-World Applications*,**6**, pp. 955-961. COSMOS Technical Report 04-03. - Rosenberger, J. M. and H. W. Corley (2004). “A Branch-and-Price Method for Solving the Smallest-World Problem.” COSMOS Technical Report 04-01.