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. Front Matter....Pages i-xvii Front Matter....Pages 1-1 Introduction....Pages 3-15 Kernelization....Pages 17-49 Bounded Search Trees....Pages 51-76 Iterative Compression....Pages 77-98 Randomized Methods in Parameterized Algorithms....Pages 99-127 Miscellaneous....Pages 129-150 Treewidth....Pages 151-244 Front Matter....Pages 245-245 Finding cuts and separators....Pages 247-284 Advanced kernelization algorithms....Pages 285-319 Algebraic techniques: sieves, convolutions, and polynomials....Pages 321-355 Improving dynamic programming on tree decompositions....Pages 357-375 Matroids....Pages 377-418 Front Matter....Pages 419-419 Fixed-parameter intractability....Pages 421-465 Lower Bounds Based on the Exponential-Time Hypothesis....Pages 467-521 Lower bounds for kernelization....Pages 523-555 Back Matter....Pages 556-613