Combinatorial Optimization, Algorithms, and Operations Research
When you want to go from a point A to another point B as fast as possible, a navigation system such as Google Map quickly tells us which route is the best. Behind this, in addition to how accurate the map data is and how fast the computers can perform procedures, the power of algorithms, which define the concrete procedures of computing, plays an important roles. To output the same result for the same input, the computational time or space of algorithms can be significantly different; for example, it is possible that one finishes within 0.1 second but another does not finish within a year. Thus, it is very important to design and select an efficient algorithm when you want to solve a problem.
I mainly study combinatorial optimization, where we want to find the "best" combination in a given criterion subject to a given constraint, such as the aforementioned routing problem. As well as considering efficient algorithms for and sometimes hardness of individual problems, I am interested in "what kind of combinatorial structures or properties make the problems easy or difficult", and investigate such a question related to discrete mathematics (graphs, matroids, submodular functions, etc.).
In the real world, there are many types of requirements, e.g., we want to assign students to laboratories (research groups) in a "fair" manner, we want to invest money with "low" risk and "high" return, and we want to design networks (for electricity distribution, transportation, or telecommunication) with "low" cost and "high" reliability. Operations research is a mathematical study for supporting decision making in such situations by formulating realistic (or sometimes unrealistic) situations as mathematical models and analyzing them. Our research group including I studies a variety of topics in operations research, which are not restricted to combinatorial optimization and discrete algorithms.
- March 2013: Master of Science from Kyoto University, Japan.
- March 2016: Doctor of Philosophy in the field of Mathematical Informatics from University of Tokyo, Japan.
- April 2016: Assistant Professor at Osaka University, Japan.
- April 2020: Associate Professor at Kyushu University, Japan.
- September 2021: Associate Professor at Osaka University, Japan.
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