Parameterized Complexity Theory - J. Flum

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Résumé :
Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability. This book is a state-of-the-art introduction to both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes, and it presents detailed proofs of recent advanced results that have not appeared in book form before. Several chapters are each devoted to intractability, algorithmic techniques for designing fixed-parameter tractable algorithms, and bounded fixed-parameter tractability and subexponential time complexity. The treatment is comprehensive, and the reader is supported with exercises, notes, a detailed index, and some background on complexity theory and logic. The book will be of interest to computer scientists, mathematicians and graduate students engaged with algorithms and problem complexity.

Biographie:
Prof. JÖrg Flum, Abteilung fÜr Mathematische Logik, Albert-Ludwigs-UniversitÄt Freiburg, Germany, http://logik.mathematik.uni-freiburg.de/personen/Flum.html Prof. Martin Grohe, Institut fÜr Informatik, Humboldt-UniversitÄt zu Berlin, Germany, http://www.informatik.hu-berlin.de/~grohe/ The authors are very well qualified to write this book. In addition to their strong backgrounds in complexity, algorithms, etc., they have contributed a number of specific key results in parameterized complexity (e.g., http://epubs.siam.org/sam-bin/dbq/article/42720). JÖrg Flum has coauthored two other Springer monographs: (i) Mathematical Logic, Undergraduate Texts in Mathematics, 0-387-94258-0, 3rd printing since 1994, over 4000 copies sold, Heinz-Dieter Ebbinghaus, JÖrg Flum, Wolfgang Thomas, http://www.springer.com/0-387-94258-0. (ii) Finite Model Theory, Springer Monographs in Mathematics (was in series Perspectives in Mathematical Logic), printed in soft- and hardback, 1995, 2nd ed. in 1999, 2nd corr. print in 2006, Heinz-Dieter Ebbinghaus, JÖrg Flum, 3-540-28787-6, http://www.springer.com/3-540-28787-6. In addition, JÖrg Flum coauthored the following LNM title: Vol. 769, Topological Model Theory, 1980, 3-540-09732-5, JÖrg Flum, Martin Ziegler. And he coedited the following LNCS title: Vol. 1683, CSL 1999 conf. proc., JÖrg Flum, Mario Rodriguez-Artalejo, 1999, 3-540-66536-6. Prof. Martin Grohe has authored over 50 articles for refereed theoretical computer science journals and conference proceedings (http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/g/Grohe:Martin.html) in the areas of logic, complexity, algorithms, etc.

Sommaire:
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A-Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability and Limited Nondeterminism.- Subexponential Fixed-Parameter Tractability.