The objective of this project is the study of algorithms and complexity, focusing on specific application areas and methodologies. This project is aimed to further our understanding of local search and some other important computational problems whose answers are guaranteed to exist. The research involves development of rigorous techniques for attacking various computational problems with an "artificial intelligence" flavor, such as prehension and exploration by robots, and probabilistic logic, a complexity-based understanding of certain aspects of Economic Theory and Game Theory, and study of problems in security and communication in very large networks, and certain novel optimization problems related to communication networks.