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Discrete Mathematics Lab
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The lab uses mathematics to find ways of choosing the best option from a vast number of combinations.
AboutAbout the lab
The best one among countless options.
The Discrete Mathematics Lab mainly studies optimization problems known as combinatorial optimization (discrete optimization).
Combinatorial optimization is a field of the foundational theory of computer science, and it is expected to find applications in many fields, including operations research, management, and economics.
From the standpoint of discrete mathematics, the lab investigates the mathematical properties of problems and develops algorithms that put the results to use in solving concrete problems.
Key terms
- Combinatorial optimization
- The problem of choosing the best one from among combinations of many options.
- Traveling salesman problem
- The problem of finding the shortest route that visits every city exactly once and returns to the starting point.
- Stable matching
- A pairing, such as people with people or people with jobs, in which no pair would want to swap partners any further.
NewsLab news
A paper by Prof. Kamiyama and colleagues was published in Discrete Optimization
A paper by Prof. Kamiyama and colleagues was published in Theoretical Computer Science
A paper by Prof. Kamiyama and colleagues was published in ACM Transactions on Economics and Computation
A paper co-authored by a doctoral student and Associate Professor Haraguchi received the Best Student Paper Award at IWOCA 2025
A paper by Prof. Kamiyama and colleagues was published in Operations Research Letters
ResearchResearch themes
From the standpoint of discrete mathematics, the lab investigates the mathematical properties of combinatorial optimization problems and develops algorithms that put the results to use in solving concrete problems.
*Illustrative imageChoosing the Best from a Vast Number of Combinations
Combinatorial optimization is the problem of choosing the best solution from among an enormous number of candidates. Algorithms for the traveling salesman problem are also useful for deciding the movements of drills that make holes in electronic circuit boards and for analyzing protein structures.
*Illustrative imageAlgorithms for Graphs and Packing Problems
The lab works on theoretical research on graph and network problems and on developing practical algorithms for packing problems. It also studies production planning, delivery planning, scheduling, game theory, and data analysis.
*Illustrative imageTheory of Stable Matching
Prof. Kamiyama has studied the theory of stable matching problems. The lab investigates topics such as strongly stable matchings under matroid constraints and matchings with non-uniform stability.
MembersFaculty
The faculty of the Discrete Mathematics Lab are Professor Naoyuki Kamiyama, Associate Professor Kazuya Haraguchi, and Assistant Professor Kanae Yoshiwatari.
- ProfessorNaoyuki Kamiyama
- Associate ProfessorKazuya Haraguchi
- Assistant ProfessorKanae Yoshiwatari
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Graph example (Graph theory)” Römert / CC BY-SA 3.0 (cropped)
- Choosing the Best from a Vast Number of Combinations: “Improvement to Travelling Salesman problem used in Article” Saurabh.harsh / CC BY 3.0 (cropped)
- Algorithms for Graphs and Packing Problems: “Circle Packing” Schluchtenbummler / CC BY-SA 4.0 (cropped)
- Theory of Stable Matching: “BipartiteFinalWiki” Pmendek / CC BY-SA 4.0 (cropped)
- Related lab (Collective Intelligence Systems Lab): “DataAppliedWeb” Marksenizer / CC BY-SA 3.0 (cropped)
- Related lab (Mathematical Information Systems Lab): “Cosine Series Plus Noise” Fourier1789 / CC BY-SA 4.0 (cropped)
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- Related lab (Intelligent Computing Lab): “Water Dolphin” JJ Harrison (https://www.jjharrison.com.au/) / CC BY-SA 3.0 (cropped)
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