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.

Table of Contents

Part I Basic toolbox
Chapter 1 Introduction
Chapter 2 Kernelization
Chapter 3 Bounded search trees
Chapter 4 Iterative compression
Chapter 5 Randomized methods in parameterized algorithms
Chapter 6 Miscellaneous
Chapter 7 Treewidth

Part II Advanced algorithmic techniques
Chapter 8 Finding cuts and separators
Chapter 9 Advanced kernelization algorithms
Chapter 10 Algebraic techniques: sieves, convolutions, and polynomials
Chapter 11 Improving dynamic programming on tree decompositions
Chapter 12 Matroids

Part III Lower bounds
Chapter 13 Fixed-parameter intractability
Chapter 14 Lower bounds based on the Exponential-Time Hypothesis
Chapter 15 Lower bounds for kernelization