In the rapidly growing world of Internet infrastructures, we face many challenging new problems. These arise in part because the usual assumptions made in problems of this general type may no longer hold. For example, many typical questions dealing with massive data sets often involve networks or graphs of prohibitively large sizes. Only partial information can be obtained and in addition, this information is changing dynamically. There is an increasing need to develop the theoretical foundation for these myriad complex processes. In particular, there are many unresolved fundamental issues regarding the computational and informational-theoretic complexity of interactive computing, both in the classical setting as well as other emerging computational paradigms. In this proposal, we will investigate several inter-related areas : - Major open problems in communication complexity. - Two information-theoretic identification problems Guessing secrets and Finding favorites. - Two directions in quantum information processing quantum decision tree model and quantum communication complexity. - Using techniques in the study of the so-called "power law model" for realistic networks to develop new methods in the analysis of on-line algorithms. Impact Interactive computing is prevalent in almost all areas of computing and communcations with applications in numerous areas of science and engineering, such as security, finance, information retrieval, bioinformatics and beyond. However, the current state of the theoretical foundation for interactive computation is quite primitive and far from satisfactory. The proposed study on the computational complexity of interactive computation is meant to strengthen our understanding and provide insight that is crucial for the design and analysis of interactive algorithms. Because of the fundamental and far-reaching nature of the proposed work, this study will help bring together different areas and crossfertilization typically occur.
