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-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.
|Publisher:||Springer International Publishing|
|Edition description:||Softcover reprint of the original 1st ed. 2015|
|Product dimensions:||6.10(w) x 9.25(h) x 0.05(d)|
About the Author
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.
Table of Contents
Introduction.- 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.
What People are Saying About This
"This is the best book yet on the subject of multivariate algorithmics for students and scientists in other fields." [Michael R. Fellows, Charles Darwin University, Australia]
"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]