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 presentscomplexity 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.

Table of Contents

Part I Basic toolbox

1 Introduction

2 Kernelization

3 Bounded search trees

4 Iterative compression

5 Randomized methods in parameterized algorithms

6 Miscellaneous

7 Treewidth

Part II Advanced algorithmic techniques

8 Finding cuts and separators

9 Advanced kernelization algorithms

10 Algebraic techniques: sieves, convolutions, and polynomials

11 Improving dynamic programming on tree decompositions

12 Matroids

Part III Lower bounds

13 Fixed-parameter intractability

14 Lower bounds based on the Exponential-Time Hypothesis

15 Lower bounds for kernelization

About the Authors

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.