My recent interests are combinatorics, algorithms and computational complexities. For example, we study the Traveling Salesman Problem. The Traveling Salesman Problem is to find a shortest Hamilton cycle in a given complete weighted digraph. The TSP is one of the most famous problems in computer science, because it belongs to the NP-hard class, that is, it is believed to be impossible to solve it in polynomial time.
So, much work has been done on algorithms to find a nearly optimal tour. Such work is often applicable to a number of practical problems.
Another direction is the study of polynomialably solvable cases, that is, to find good conditions on the distances that insure there is an algorithm which finds an optimal tour in polynomial time. My research mainly deals with the latter from the view point of combinatorics.
The Monge property is well-known as a special case of the Traveling Salesman Problem. I have found several special cases which are extensions of the Monge property, and presented some classes of Hamilton cycles, and constructed algorithms to find a shortest Hamilton cycle in those classes.
I am also interested in graph theory and discrete geometry, e.g. Voronoi diagrams and Delaunay triangulations.