Parameterized Algorithms

This 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.

• Branching
• Fixed-parameter tractability (FPT);
• Integer linear programming (ILP)
• Kernels
• Matroids
• Parameterized algorithms
• Parameterized complexity
• Treewidth
• algorithm analysis and problem complexity

“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)

"It's a great contribution to the community ... many people should read this." [Philip Klein, Brown University, USA]

"The book is very accessible and provides a clear road map for learning about parametrized complexity. It neatly summarizes the main results of the last decade." [Gerhard Woeginger, TU Eindhoven, The Netherlands]

"This is a timely book written by experts who have contributed heavily to recent developments ... a very valuable resource to students and researchers interested in parameterized complexity. Ample and well-chosen exercises make it particularly useful in teaching a one- or two-semester course. The book has many topics of interest to the broader community of researchers in (theoretical) computer science. It is a welcome addition to the literature." [Chandra Chekuri, University of Illinois, Urbana-Champaign, USA]

• Institute of Informatics, University of Warsaw, Warsaw, Poland

  Marek Cygan, Łukasz Kowalik, Marcin Pilipczuk, Michał Pilipczuk

• Dept. of Informatics, University of Bergen, Bergen, Norway

  Fedor V. Fomin

• Department of Informatics, University of Bergen, Bergen, Norway

  Daniel Lokshtanov

• Inst. for Computer Science & Control, Hungarian Academy of Sciences, Budapest, Hungary

  Dániel Marx

• C.I.T. Campus, The Institute of Mathematical Sciences, Chennai, India

  Saket Saurabh

Dr. Marek Cygan is an assistant professor at the Institute of Informatics of the University of Warsaw, Poland. His research areas include fixed parameter tractability, approximation algorithms, and exact exponential algorithms.

Prof. Fedor V. Fomin is a professor of algorithms in the Dept. of Informatics of the University of Bergen, Norway. His research interests are largely in the areas of algorithms and combinatorics, in particular: parameterized complexity, algorithms, and kernelization; exact (exponential time) algorithms; graph algorithms, in particular algorithmic graph minors; graph coloring and different modifications; graph widths parameters (treewidth, branchwidth, clique-width, etc.); and pursuit-evasion and search problems.

Dr. Hab. Łukasz Kowalik is an associate professor at the Institute of Informatics of the University of Warsaw, Poland. His research areas include algorithms and graph theory, in particular approximation algorithms, exact algorithms for NP-hard problems, planar graphs, and graph coloring.

Dr. Daniel Lokshtanov is a junior faculty member of the Dept. of Informatics of the University of Bergen, Norway. His research focuses on algorithmic graph theory, and he is the project leader for BeHard, a research project on kernelization.

Dr. Dániel Marx is a senior research fellow at the Institute for Computer Science and Control (SZTAKI) of the Hungarian Academy of Sciences, Budapest, Hungary. His research areas include discrete algorithms, parameterized complexity, and graph theory.

Dr. Marcin Pilipczuk is a postdoctoral researcher at the Institute of Informatics of the University of Warsaw, Poland. His research focuses on algorithmics, especially fixed parameter tractability and exact computations of NP-hard problems.

Dr. Michał Pilipczuk is a postdoctoral researcher at the Institute of Informatics of the University of Warsaw, Poland. His research areas include parameterized complexity, moderately exponential-time algorithms, and kernelization.

Prof. Saket Saurabh is a member of the Theoretical Computer Science (TCS) group of The Institute of Mathematical Sciences (CIT Campus) in Chennai, India. His research interests include algorithms and graph theory, in particular, parameterized and exact algorithms.

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