Abstract: The maximum entropy method (MEM) is a relatively new technique for solving underdetermined systems. It has been successfully applied in many different areas. All methods for solving underdetermined systems introduce some additional, artificial constraints. The advantage of the maximum entropy method is that it uses the most natural additional constraint: one that does not introduce any new, arbitrary and unwarranted information. One important property of entropy maximization is that it favors uniform distribution.
Network design and analysis almost always involve underdetermined systems, especially when routing policy has to be determined. The number of possible routings grows with the factorial of the number of the nodes in the network and the number of possible topologies is exponential in the number of links. The number of constraints is typically polynomial in the number of nodes in the network. That makes the network design problem a good candidate for the maximum entropy method application. It is intuitively clear that an optimal network should not have overloaded or underutilized links. The hope is that the maximum entropy constraint will give a starting topology and routing with smoothly distributed traffic that would lead to the solution that is closer to the optimal. The problem is computationally feasible and with proper identification and selection of certain parameters the method gives reasonable topology and routing.
It is possible to apply MEM if we start our analysis with totally interconnected network of n nodes. Some lines will be dropped later in the process of improving utilization or reducing the cost. To apply the maximum entropy method we have to decide what will be the variables of the system. Some combination of required traffic values can be used for that if we remember that for MEM application we do not need to start with probabilities, but an arbitrary set of numbers which can be normalized. Additional parameters are introduced which allow the control of optimization process.
Philosophical discussions about the real meaning of the maximum entropy method are interesting, but since the method was successfully applied in many areas, for any new area the most important criterion is not how well can we explain the relation between the MEM and that area, but how useful are the results we get by applying the method.


Brief Biography of the Speaker:
Milan Tuba received B. S. in Mathematics, M. S. in Mathematics, M. S. in Computer Science, M. Ph. in Computer Science, Ph. D. in Computer Science from University of Belgrade and New York University. From 1983 to 1987 he was a graduate student and teaching and research assistant at Vanderbilt University in Nashville and Courant Institute of Mathematical Sciences, New York University. From 1987 to 1993. he was Assistant Professor of Electrical Engineering at Cooper Union Graduate School of Engineering, New York. During that time he was the founder and director of Microprocessor Lab and VLSI Lab, leader of scientific projects and supervisor of many theses. From 1994 he was Associate professor of Computer Science and Director of Computer Center at University of Belgrade, Faculty of Mathematics, and from 2004 also Professor of Computer Science and Dean of the College of Computer Science, Megatrend University Belgrade. He was teaching about 20 graduate and undergraduate courses, from VLSI Design and Computer Architecture to Computer Networks, Image Processing, Calculus and Queuing Theory. His research interest include mathematical, queuing theory and algorithmic optimizations applied in computer networks, image processing and combinatorial problems. He is the author of more than 60 scientific papers and a monograph. He was coeditor or member of the board of editors of number of scientific journals and conferences. Member ACM 1983, IEEE 1984, AMS 1995, New York Academy of Sciences 1987.