2019年度 グラフ理論とその応用   Graph Theory with Engineering Application

文字サイズ 

アップデートお知らせメールへ登録 お気に入り講義リストに追加
開講元
工学院
担当教員名
WIMER SHMUEL  高橋 篤司 
授業形態
講義
曜日・時限(講義室)
月3-4(S322)  
クラス
-
科目コード
XEG.S404
単位数
1
開講年度
2019年度
開講クォーター
3Q
シラバス更新日
2019年3月18日
講義資料更新日
2019年11月11日
使用言語
英語
アクセスランキング

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

国際的教養力 コミュニケーション力 専門力 課題設定力 実践力または解決力
- - - -

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 Introduction representations, isomorphism, graph structures, trees, flows, connectivity, transitivity, 3-connected graphs.
第2回 Matching maximum matching, bipartite graphs, perfect matching, matching algorithms.
第3回 Graph coloring vertex coloring, the chromatic number, perfect graphs, map coloring, edge coloring.
第4回 Connectivity vertex connectivity, edge connectivity, 3-connected graphs.
第5回 The probabilistic method random graphs, expectation, variance, evolution of random graphs.
第6回 Planar graphs Jordan curve, duality, Euler formula, bridges, planarity recognition, the four-color problem.
第7回 Graphs and matrices adjacency and incidence, eigenvectors, ranks, symmetric graphs.
第8回 Electrical networks circulations and tensions, the matrix-tree theorem, resistive electrical networks, perfect squares, random walks on graphs.

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

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

このページのトップへ