Classical computer science textbooks tell us that some problems are 'hard'. Yet many areas, from machine learning and computer vision to theorem proving and software verification, have defined their own set of tools for effectively solving complex problems. Tractability provides an overview of these different techniques, and of the fundamental concepts and properties used to tame intractability. This book will help you understand what to do when facing a hard computational problem. Can the problem be modelled by convex, or submodular functions? Will the instances arising in practice be of low treewidth, or exhibit another specific graph structure that makes them easy? Is it acceptable to use scalable, but approximate algorithms? A wide range of approaches is presented through self-contained chapters written by authoritative researchers on each topic. As a reference on a core problem in computer science, this book will appeal to theoreticians and practitioners alike.

About the Authors

Lucas Bordeaux is a Senior Research Software Development Engineer at Microsoft Research, Cambridge, where he works on the design and applications of algorithms to solve hard inference problems.

Youssef Hamadi is a Senior Researcher at Microsoft Research, Cambridge. His work involves the practical resolution of large-scale real life problems set at the intersection of Optimization and Artificial Intelligence. His current research considers the design of complex systems based on multiple formalisms fed by different information channels which plan ahead and perform smart decisions. His current focus is on Autonomous Search, Parallel Search, and Propositional Satisfiability, with applications to Environmental Intelligence, Business Intelligence, and Software Verification.

Pushmeet Kohli is a Research Scientist in the Machine Learning and Perception group at Microsoft Research, Cambridge. His research interests span the fields of Computer Vision, Machine Learning, Discrete Optimization, Game Theory, and Human-Computer Interaction with the overall aim of 'teaching' computers to understand the behaviour and intent of human users, and to correctly interpret (or 'See') objects and scenes depicted in colour/depth images or videos. In the context of tractability and optimization, Pushmeet has worked on developing adaptive combinatorial and message passing-based optimization algorithms that exploit the structure of problems to achieve improved performance.

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