2021年度 グラフ理論とその応用   Graph Theory with Engineering Application

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開講元
工学院
担当教員名
WIMER SHMUEL  高橋 篤司 
授業形態
講義    (ZOOM)
曜日・時限(講義室)
月3-4  
クラス
-
科目コード
XEG.S404
単位数
1
開講年度
2021年度
開講クォーター
3Q
シラバス更新日
2021年4月2日
講義資料更新日
-
使用言語
英語
アクセスランキング
media

講義の概要とねらい

Graph theory results are widely used to model and solve many engineering, social and natural science problem; it is also an excellent mean to explore proof techniques in discrete mathematics. This course aims at introducing basic graph theory concepts, and it demonstrates how they can be used in facing real-life modeling and design problem.

到達目標

The main goal of this course is to equip the students with graph theory “state of mind” in facing engineering problems. The students will acquire graph theory basic knowledge and will experiencing solutions to some common problems, which will direct them towards utilizing analytical approach in their R&D challenges, in addition to simulation and experiments, which are commonly used in R&D.

キーワード

Graph theory, Algorithms, Complexity, Linear algebra, Combinatorics, and Probability

学生が身につける力(ディグリー・ポリシー)

専門力 教養力 コミュニケーション力 展開力(探究力又は設定力) 展開力(実践力又は解決力)

授業の進め方

This course aims at introducing basic graph theory concepts, and it demonstrates how they can be used in facing real-life modeling and design problem. Its approach it a mix of formal and intuition, where no previous knowledge in graph theory is assumed. There will be formal proofs of some important theorems (though few), while others will only be overviewed. Algorithms and complexity will only be briefly discussed as those are widely covered in other courses. Each of the topics will demonstrate related practical problems.

授業計画・課題

  授業計画 課題
第1回 Matching Maximum matching, bipartite graphs.
第2回 Matching (cont’d) Perfect matching, matching algorithms.
第3回 Cliques and independent sets Shannon capacity, Turán’s theorem, Ramsey’s theorem.
第4回 Graph coloring Vertex coloring, the chromatic number, perfect graphs, map coloring, edge coloring.
第5回 Connectivity Vertex connectivity, edge connectivity, 3-connected graphs.
第6回 Planar graphs Duality, Euler formula, bridges, planarity recognition, the four-color problem.
第7回 The probabilistic method Random graphs, expectation, variance, evolution of random graphs.

授業時間外学修(予習・復習等)

学修効果を上げるため,教科書や配布資料等の該当箇所を参照し,「毎授業」授業内容に関する予習と復習(課題含む)をそれぞれ概ね100分を目安に行うこと。

教科書

None

参考書、講義資料等

All lectures slides will be available on-line.

J.A. Bondy and U.S.R. Murty, Graph Theory, Springer.
D.B. West, Introduction to Graph Theory, Prectice-Hall.

成績評価の基準及び方法

Learning achievement is evaluated by the quality of the written reports, exercise problems, and etc.

関連する科目

  • XEG.S405 : ディジタルVLSI設計
  • XEG.S605 : ディジタルVLSI設計特論
  • XEG.S406 : 計算機アーキテクチャ(工学院)
  • XEG.S607 : 計算機アーキテクチャ特論(工学院)

履修の条件(知識・技能・履修済科目等)

Students are supposed to have some background in algorithms, basic knowledge of linear algebra, combinatorics and probability.

連絡先(メール、電話番号)    ※”[at]”を”@”(半角)に変換してください。

atsushi [at] ict.e.titech.ac.jp

オフィスアワー

Contact by e-mail in advance to schedule an appointment

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