# Research

Our laboratory focuses on "algorithms", "discrete mathematics", and their applications. In particular, we plan to study the following topics, focusing mainly on "graphs".

- 1. Develop theoretically fast and accurate algorithms for graph problems or prove NP-hardness for them
- 2. Develop scalable and accurate algorithms that can be implemented, using theoretical tools such as discrete mathematics, for graph datasets in the real world.
- 3. Develop algorithms that can run theoretically (or practically) quite fast (and accurate), when limiting graph family (for example, planar graphs or social networks).
- 4. Apply knowledge and implementation techniques of graph algorithms to machine learning, especially online learning and deep learning.
- 5. Research on graphs that appear in the fields of natural language processing, machine learning, databases, data mining, programming languages, etc.
- 6. Combinatorial optimization and/or discrete mathematics

In our laboratory, we plan to interact with top researchers for theory in overseas for the above "theoretical" research, and jointly work with researchers in Japan and overseas, including industries, for other research topics.

Algorithm innovations such as current information retrieval technology (Google's PageRank) and security technology (Apple's (Local) Different Privacy) have led to the creation of national-scale businesses. What is important here is that both PageRank and Differential Privacy are basic and theoretical researches of algorithms and discrete mathematics, not application-oriented work from the beginning. In our laboratory as well, we plan to focus on basic and theoretical research, rather than conducting research with applications in mind from the beginning.

Email : k_keniti[at]nii.ac.jp

※please replace the [at] with a proper @