Fundamentals of Parameterized Complexity

Abstract

The field of parameterized complexity/multivariate complexity algorithmicsis an exciting and vibrant part of theoretical computer science,responding to the vital need for efficient algorithms in modern society.This comprehensive and self-contained textbook presents an accessibleoverview of the state of the art of multivariate algorithmics andcomplexity. Increasingly, multivariate algorithmics is having significantpractical impact in many application domains, with even more developmentson the horizon. The text describes how the multivariate frameworkallows an extended dialog with a problem, enabling the reader whomasters the complexity issues under discussion to use the positiveand negative toolkits in their own research.Topics and features:Describes many of the standard algorithmic techniques available forestablishing parametric tractabilityReviews the classical hardness classesExplores the various limitations and relaxations of the methodsShowcases the powerful new lower bound techniquesExamines various different algorithmic solutions to the same problems,highlighting the insights to be gained from each approachDemonstrates how complexity methods and ideas have evolved over thepast 25 yearsThis classroom-tested and easy-to-follow textbook/reference is essentialreading for the beginning graduate student and advanced undergraduatestudent. The book will also serve as an invaluable resource for thegeneral computer scientist and the mathematically-aware scientistseeking tools for their research.