As the world is flooded with data, the demand for mining data for useful purposes is increasing. An effective techniques is to model the data as networks (graphs) and then apply graph mining techniques for analysis. As on date, the algorithms available to count graphlets and orbits for various types of graphs and their generalizations are limited. The thesis aims to fill the gap by presenting a simple and efficient algorithm for 3-node graphlet and orbit counting that is generic enough to work for both undirected and directed graphs. Our algorithm is compared with the state-of-art algorithms and we show that in most cases our algorithm performs better. We demonstrate our algorithm in three case studies related to (i) enzyme and metabolite correlation network in corn, (ii) watershed governance networks, and (iii) patterns exhibited by co-expression networks of healthy and cancerous stomach cells.
The design of efficient control strategies is a well studied problem. Due to recent technological advancements and applications in the field of robotics, exploring novel ways to design optimal control for multi-robot systems has gained interest. In this respect, the concept of ergodicity has successfully been applied as an effective control technique for tracking and area coverage. The generation of flocking behaviour is a problem that involves both tracking and coverage, and as such is also suited for the use of ergodicity. The main contribution of this thesis is the application of ergodicity to emulate flocking behaviour. This approach is appealing because control and communication is assumed to be local, self-organized, and does not require separate algorithms in order to generate different behaviour. Simulation results show that the proposed approach is effective and a prototype provides evidence that flocking behaviour is possible using ergodicity in a real-life setting.
