The topic of parameterized algorithms is one of the main subjects in modern computer science. In this type of algorithm analysis, the running time is a function of the size of the input data and of a set of one or more parameters. The theory of parameterized algorithms originated in late 1980 when the first systematic explorations of this class of algorithms began. However, the fast development of the field caused many classic texts (on the subject) to age quickly, as they did not cover most modern algorithm results, tools, and techniques. In this sense Parameterized algorithms aims to discuss some of the most advanced and novel algorithms in the field such as algorithms for important separators, algorithms for linear programming, algorithms based on representative families of matroids, algorithms related to use of the strong exponential time hypothesis (SETH), and algorithms for faster tree decomposition.

The covered material is divided into three parts. The first part, “Basic Toolbox” (chapters 1 to 7), is introductory, presenting the main algorithmic techniques. In other words, it is designed to be used as an introductory text on the topic of fixed-parameter tractability. In this part, each chapter discusses one algorithm in fair detail. It is very significant to mention, and is a big plus to the book, that each chapter ends with an abundance of exercises (both hard and easy). These, along with hints and some bibliographic notes, make the book self-contained and suitable for self-study for advanced undergraduates.

The second part of the book (chapters 8 to 12) covers advanced algorithmic techniques, which may interest a reader who wants a quick introduction to the most novel algorithms and techniques. As such, the second part may serve advanced users well. Because of its advanced level, each chapter has fewer but more difficult exercises, along with more hints, to provoke independent problem solving.

The last part (chapters 13 to 15) is devoted to special topics. Here, the interested reader could find the evidence that certain problems are not fixed parameter tractable, along with techniques and tools used to show the lower bounds for algorithms discussed before.

The style of the book is clear, and the material is well positioned to be accessible by graduate students and advanced undergraduate students. The exercises and hints provide a good ground for self-study, while bibliographic notes point to original papers and related work.

Overall, this is an excellent book that can be useful to graduate and advanced undergraduate students either as a self-study text or as part of a course.