Tractability: Practical Approaches to Hard Problems

doi:10.1017/CBO9781139177801

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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-x
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Contributors
pp xi-xii
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Introduction
pp xiii-xxii
- By Lucas Bordeaux, Microsoft Research , Youssef Hamadi, Microsoft Research , Pushmeet Kohli, Microsoft Research
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Part 1 - Graphical Structure
pp 1-2
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1 - Treewidth and Hypertree Width
pp 3-38
- By Georg Gottlob, University of Oxford, Gianluigi Greco, Università degli Studi della Calabria, Francesco Scarcello, University of Calabria
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2 - Perfect Graphs and Graphical Modeling
pp 39-68
- By Tony Jebara, Columbia University
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Part 2 - Language Restrictions
pp 69-70
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3 - Submodular Function Maximization
pp 71-104
- By Andreas Krause, Universitätstrasse 6, 8092 Zurich, Daniel Golovin, Google, Inc., Mountain View CA 94043, USA
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4 - Tractable Valued Constraints
pp 105-140
- By Peter G. Jeavons, University of Oxford, Stanislav Živný, University of Oxford
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5 - Tractable Knowledge Representation Formalisms
pp 141-172
- By Adnan Darwiche, University of California Los Angeles
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Part 3 - Algorithms and their Analysis
pp 173-174
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6 - Tree-Reweighted Message Passing
pp 175-201
- By Vladimir Kolmogorov, Institute of Science and Technology
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7 - Tractable Optimization in Machine Learning
pp 202-230
- By Suvrit Sra, Max Planck Institute for Intelligent Systems
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8 - Approximation Algorithms
pp 231-259
- By Mohit Singh, Microsoft Research, Kunal Talwar, Microsoft Research Silicon Valley
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9 - Kernelization Methods for Fixed-Parameter Tractability
pp 260-282
- By Fedor V. Fomin, Universitetet i Bergen, Saket Saurabh, Institute of Mathematical Sciences
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Part 4 - Tractability in Some Specific Areas
pp 283-284
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10 - Efficient Submodular Function Minimization for Computer Vision
pp 285-303
- By Pushmeet Kohli, Microsoft Research
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11 - Towards Practical Graph-Based, Iteratively Decoded Channel Codes: Insights through Absorbing Sets
pp 304-328
- By Lara Dolecek, University of California Los Angeles
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Part 5 - Heuristics
pp 329-330
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12 - SAT Solvers
pp 331-349
- By Joao Marques-Silva, University College Dublin, Ines Lynce, Technical University of Lisbon
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13 - Tractability and Modern Satisfiability Modulo Theories Solvers
pp 350-377
- By Nikolaj Bjørner, Microsoft Research, Leonardo de Moura, Microsoft Research
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Tractability

Practical Approaches to Hard Problems

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Contents

Frontmatter
pp i-iv

Contents
pp v-x

Contributors
pp xi-xii

Introduction
pp xiii-xxii

Part 1 - Graphical Structure
pp 1-2

1 - Treewidth and Hypertree Width
pp 3-38

2 - Perfect Graphs and Graphical Modeling
pp 39-68

Part 2 - Language Restrictions
pp 69-70

3 - Submodular Function Maximization
pp 71-104

4 - Tractable Valued Constraints
pp 105-140

5 - Tractable Knowledge Representation Formalisms
pp 141-172

Part 3 - Algorithms and their Analysis
pp 173-174

6 - Tree-Reweighted Message Passing
pp 175-201

7 - Tractable Optimization in Machine Learning
pp 202-230

8 - Approximation Algorithms
pp 231-259

9 - Kernelization Methods for Fixed-Parameter Tractability
pp 260-282

Part 4 - Tractability in Some Specific Areas
pp 283-284

10 - Efficient Submodular Function Minimization for Computer Vision
pp 285-303

11 - Towards Practical Graph-Based, Iteratively Decoded Channel Codes: Insights through Absorbing Sets
pp 304-328

Part 5 - Heuristics
pp 329-330

12 - SAT Solvers
pp 331-349

13 - Tractability and Modern Satisfiability Modulo Theories Solvers
pp 350-377

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Practical Approaches to Hard Problems

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