In my research, I study problems that arise in graph theory and related areas, often motivated by applications in current network technologies such as high-speed networks, communication algorithms for these networks, and in algorithmic aspects of fault tolerance. These areas are currently enjoying a particularly high level of research activity.
I am interested in the existence of Hamilton cycles and paths in graphs. Such problems are of interest in interconnection networks and parallel architectures. In particular, my investigation is aimed at sufficient conditions for the existence of such cycles/paths, and at various modifications (pancyclicity, edge-disjoint cycles, …) of the basic problem.
Among problems arising in communication networks, I am interested in mobile networks and optical networks. My interest in theoretical cost models for mobile (ad-hoc) networks is motivated by the fact that most previous work is experimental with little qualitative analyses. The basic problem in optical networks is to design a routing schemes for given communication pattern. This is a challenging combinatorial problem and it utilizes different techniques from areas like algebraic combinatorics, graph coloring, etc. Further, I am interested in algorithmic aspects of fault tolerance on these models.
Another current area of interest is the phylogenetics--finding the genetic connections and relationships between species. The field has exploded in recent years with the realization that much of the DNA and protein structure is actually mathematical in nature. I am interested in problems linked to DNA parsimony, as well as in DNA/protein sequence analyses. The DNA parsimony is closely related to the well-known tree minor concept in graph theory. I am also interested in the computational aspects of these problems.