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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.
List of contents
Chapter 1: Introduction.- Chapter 2: Basic Techniques.- Chapter 3: Strings.- Chapter 4: Graphs in the Adjacency Metrix Model.- Chapter 5: Graphs in the Bounded-Degree Model.- Chapter 6: Functions over Hypercubes.- Chapter 7: Massively Parameterized Model.- Chapter 8: Vectors and Matrices over the Reals.- Chapter 9: Graphs in the Adjacency Matrix Model.- Chapter 10: Graphs in the Bounded-Degree Model.- Chapter 11: Affine-Invariant Properties of Functions.- Chapter 12: Linear Properties of Functions.- Chapter 13: Massively Parameterized Model.
About the author
Arnab Bhattacharyya obtained his Ph.D. from the Massachusetts Institute of Technology in 2012 and is currently an assistant professor at the National University of Singapore. He is a recipient of the Singapore National Research Foundation Fellowship for AI (2019) and the Ramanujan Fellowship in India (2014). His research area is in the theoretical foundations of data science. Yuichi Yoshida received a Ph.D. from Kyoto University in 2012 and is currently an associate professor at National Institute of Informatics, Japan. He is awarded JSPS Ikushi Prize in 2012 and the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology (The Young Scientists' Prize) in 2017. His research interest is theoretical foundation of big data.
Report
"I believe that the book has lot to offer for readers interested in property testing. ... I will recommend this book as a reference to advanced graduate students. ... I personally learnt a lot from this book ... and I firmly believe that this book will be a great reference to a researcher who wants to know more on this topic or related topics." (Sarvagya Upadhyay, SIGACT News, Vol. 54 (2), 2023)
