Seminar at SMU Delhi

In this talk we will consider three problems related to the study of random graphs and stochastic processes defined on them. The problems are as follows: \\ \noindent 1. Virus spread on a finite network; \noindent 2. Nearest neighbor algorithm for mean field traveling salesman problem; and \noindent 3. Random geometric graphs with Cantor distributed vertices. \\ \noindent The first problem is directly related to application of general random graph theory to the spread of a virus or malware in a network which is of interest in epidemiology or computer networking. The second problem is related to a famous combinatorial optimization problem known as TRAVELING SALESMAN PROBLEM and the model we consider arises from statistical physics. We study a specific approximation algorithm for this traveling salesman problem and try to study its performance. The third and the last problem is related to the study of certain types of random graphs. We study a curious case of RANDOM GEOMETRIC GRAPHS and show that the standard results may not hold when we differ from the usual assumption in the theory of random geometric graphs. \\ \noindent [The talk is based on three joint papers with my Ph.D. supervisor Antar Bandyopadhyay]