2017 Combinatorial Algorithms

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Sumita Hanna  Fukuda Mituhiro  Yamashita Makoto 
Course component(s)
Day/Period(Room No.)
Mon7-8(W834)  Thr7-8(W834)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

This course will cover representative combinatorial optimization problems and their solutions which are present in real world situations. Representative combinatorial optimization problems and their applications are extractions of the most vital part of these problems and each of them are difficult in their own way. Also, they can be extended to cover several other problems. Additionally, their solutions involve ideas and algorithms of combinatorial optimization, and mostly depend on data structure. Therefore, it will require an overall approach involving all of this knowledge. Also, the instructor will explain some technical issues and details for implementing these algorithms.

Student learning outcomes

Through this course, students will be able to recognize the representative combinatorial optimization problems which are present in real world situations and have a vague idea of their solutions. Also, they will be able to explain roughly the data structure, techniques, and constraints when implementing them to solve the problems.


Shortest path problem, dynamic programming, minimum cost flow problem, branch-and-bound method, matching, enumeration algorithms, scheduling, assignment problem, modeling

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

In each class, the instructor will give concrete examples for corresponding applications to explain the method and for students to understand its importance.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Combinatorial optimization and approximation methods Evaluation of the grade will be explained
Class 2 Dynamic programming and its applications
Class 3 Enumeration problem and its solution
Class 4 Assignment problem and its applications
Class 5 Minimum flow and production planning
Class 6 Class forming problem
Class 7 Delivery planning
Class 8 Optimization in financial engineering
Class 9 Scheduling
Class 10 Data mining
Class 11 Practical shortest path method
Class 12 Algorithms in genome science
Class 13 Sport scheduling
Class 14 Recent topics
Class 15 Recent topics



Reference books, course materials, etc.

Tetsuo Ichimori, "Mathematical Programming - Methods of Optimization'', Kyoritsu-Shuppan, ISBN-13: 978-4320014749.
Hiroshi Konno, "Financial Engineering (1) - Mean/Variance Model and its Extensions'', Nikkagirenn, ISBN-13: 978-4817150257.
Hiroshi Konno, "Introduction to Mathematical Decisions - Operations Research in the Campus'', Asakura-Shoten, ISBN-13: 978-4254126082.
Hidetoshi Ibaraki, "Discrete Optimization and Algorithms'', (Iwanami Kouza Ouyou Suugaku) Iwanami-Shoten, ISBN4-00-010805-0 C3341.

Assessment criteria and methods

Will be decided based on reports and assignments.

Related courses

  • MCS.T302 : Mathematical Optimization

Prerequisites (i.e., required knowledge, skills, courses, etc.)

It is preferred that the credits for "Mathematical Optimization'' is already obtained.

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