Description
Book SynopsisThis comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way.
The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds.
All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
Trade Review“I enjoyed reading this book, which is a good textbook for graduate and advanced undergraduate students of computer science. Each chapter contains sufficient exercises with hints whenever necessary and helpful bibliographic notes. I found the references quite comprehensive, and the index was quite useful. … this is the best book I have seen on the topic. I strongly recommend it.” (Soubhik Chakraborty, Computing Reviews, April, 2017)
“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.” (Alexander Tzanov, Computing Reviews, February, 2016)
“This is the most recent and most up-to-date textbook on parameterized algorithms, one of the major thrusts in algorithmics in recent years. … this new textbook has more than twice as many pages shows the development of the field. … This book does a very good job at balancing the necessary mathematical rigour with a nice presentation of the results.” (Henning Fernau, Mathematical Reviews, February, 2016)
“This book serves as an introduction to the field of parameterized algorithms and complexity accessible to graduate students and advanced undergraduate students. It contains a clean and coherent account of some of the most recent tools and techniques in the area.” (Paulo Mbunga, zbMATH 1334.90001, 2016)
Table of ContentsIntroduction.- Kernelization.- Bounded Search Trees.- Iterative Compression.- Randomized Methods in Parameterized Algorithms.- Miscellaneous.- Treewidth.- Finding Cuts and Separators.- Advanced Kernelization Algorithms.- Algebraic Techniques: Sieves, Convolutions, and Polynomials.- Improving Dynamic Programming on Tree Decompositions.- Matroids.- Fixed-Parameter Intractability.- Lower Bounds Based on the Exponential-Time Hypothesis.- Lower Bounds for Kernelization.
