The aim of research is to develop a novel geometric framework in order to provide deep insights into the elemental limitations and trade-offs involved in efficient and dependable network routing. I intend to uncover, in a very illustrative manner, how traffic instances compete for network resources and how users affect each other's traffic in a resource constrained network, and how to provision forwarding paths as to minimize the interference. The basic idea is to view networks and routing protocols in a completely new way, by assigning simple geometric objects to them and studying their interaction through observing the geometric properties thereof. This approach opens up a plethora of new possibilities in modeling, mathematical analysis, algorithm design, and numeric methods, as it augments the existing, fundamentally algebraic theoretical toolset, like the theory of network flows, linear programming, etc., with a new, inherently geometric point of view. This approach has already proved itself remarkably fruitful in answering some open questions in network theory, like for instance deciding whether a routing independent max-min fair resource allocation exists in every network. Consequently, it is my belief that, provided that the theoretical and practical underpinnings are worked out in full glory, the proposed framework for network geometry can give a uniquely capable tool in the hands of the networking community.
Project leader (TMIT):