This course will cover representative combinatorial optimization problems and their methods to solve the problems. Real world problems are modeled as optimization problems by extracting the vital constraints and objectives. It is practically important to solve the optimization problems efficiently. For this end, we need to investigate and utilize a specific property and structure of each problem. This course describes fundamental "combinatorial" optimization problems and their algorithms using their own properties. In addition, this course explains the theory on combinatorial structures and algorithms.
The aim of this course is to give knowledge on fundamental combinatorial optimization problems and their algorithms, and give mathematical tools to argue the performance of the algorithms.
By the end of this course, students will be able to:
1) Recognize fundamental combinatorial optimization problems appearing in real world situations.
2) Have a vague idea of methods to solve those combinatorial optimization problems.
3) Explain roughly the performance of methods from a theoretical perspective.
combinatorial optimization, algorithm, dynamic programming, minimum cost flow problem, matching, matroid, submodular, modeling
|Intercultural skills||Communication skills||✔ Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Basically each class focuses on one combinatorial optimization problem. Students learn its applications and methods to solve the problem.
|Course schedule||Required learning|
|Class 1||Introduction to combinatorial optimization||Evaluation of the grade will be explained|
|Class 2||Maximum matching problem|
|Class 3||Maximum flow problem|
|Class 4||Minimum flow problem|
|Class 5||Stable marriage problem|
|Class 7||Knapsack problem and approximation algorithm|
|Class 8||Knapsack problem and dynamic programming|
|Class 9||Traveling salesman problem|
|Class 10||Submodular maximization problem|
|Class 11||Enumeration problem|
|Class 12||Online problem|
|Class 13||Secretary problem|
|Class 14||Recent topics|
|Class 15||Recent topics|
B. Korte and J. Vygen, "Combinatorial Optimization: Theory and Algorithms", Springer, 2018.
M. Shigeno, "Network Optimization and Algorithms （ネットワーク最適化とアルゴリズム)", Asakura-Shoten, 2010. (Japanese)
Y. Kawahara and K. Nagano, "Submodular Optimization and Machine Learning (劣モジュラ最適化と機械学習)", Kodansya, 2015. (Japanese)
All course materials will be uploaded on OCW-i.
Students will be assessed on the final report and assignments.
No prerequisites are necessary, but enrollment in the related course (Mathematical Optimization) is desirable.