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.
Contributors; Introduction Lucas Bordeaux, Youssef Hamadi and Pushmeet Kohli; Part I. Graphical Structure: 1. Treewidth and hypertree width Georg Gottlob, Gianluigi Greco and Francesco Scarcello; 2. Perfect graphs and graphical modeling Tony Jebara; Part II. Language Restrictions: 3. Submodular function maximization Andreas Krause and Daniel Golovin; 4. Tractable valued constraints Peter G. Jeavons and Stanislav Zivny; 5. Tractable knowledge representation formalisms Adnan Darwiche; Part III. Algorithms and their Analysis: 6. Tree-reweighted message passing Vladimir Kolmogorov; 7. Tractable optimization in machine learning Suvrit Sra; 8. Approximation algorithms Mohit Singh and Kunal Talwar; 9. Kernelization methods for fixed-parameter tractability Fedor V. Fomin and Saket Saurabh; Part IV. Tractability in Some Specific Areas: 10. Efficient submodular function minimization for computer vision Pushmeet Kohli; 11. Towards practical graph-based, iteratively decoded channel codes: insights through absorbing sets Lara Dolecek; Part V. Heuristics: 12. SAT solvers Joao Marques-Silva and Ines Lynce; 13. Tractability and modern satisfiability modulo theories solvers Nikolaj Bjorner and Leonardo de Moura.