Books/Book Chapters

スペクトルグラフ理論 線形代数からの理解を目指して 𠮷田悠一 サイエンス社 2024年

スペクトルグラフ理論は，グラフという組合せ的対象を線形代数という代数的道具を用いて考察する，応用分野でも広く使われる重要な理論である．本書では，スペクトルグラフ理論の数学的な側面に注目し，理論計算機科学においてよく知られていることや，最近得られた結果を中心に解説する．また必要に応じて理論的成果がいかに応用分野で使われているかについても言及している．

Property Testing Problems and Techniques. Arnab Bhattacharyya and Yuichi Yoshida. Springer Singapore 2022.

This book introduces important results and techniques in property testing, where the goal is to design algorithms that decide whether their input satisfies a predetermined property in sublinear time, or even in constant time – that is, time is independent of the input size. This book consists of three parts. The first part provides an introduction to the foundations of property testing. The second part studies the testing of specific properties on strings, graphs, functions, and constraint satisfaction problems. Vectors and matrices over real numbers are also covered. The third part is more advanced and explains general conditions, including full characterizations, under which properties are constant-query testable.

The first and second parts of the book are intended for first-year graduate students in computer science. They should also be accessible to undergraduate students with the adequate background. The third part can be used by researchers or ambitious graduate students who want to gain a deeper theoretical understanding of property testing.