Tractability : practical approaches to hard problems /

An overview of the techniques developed to circumvent computational intractability, a key challenge in many areas of computer science.

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Bibliographic Details
Other Authors: Bordeaux, Lucas (Editor), Hamadi, Youssef (Computer science researcher) (Editor), Kohli, Pushmeet (Editor)
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 2014.
Subjects:
Online Access:CONNECT
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Table of Contents:
  • Cover
  • Tractability
  • Title Page
  • Copyright Page
  • Contents
  • Contributors
  • Introduction
  • Part 1: Graphical Structure
  • 1 Treewidth and Hypertree Width
  • 1.1 Treewidth
  • 1.2 Hypertree width
  • 1.3 Applications of hypertree width
  • 1.4 Beyond (hyper)tree decompositions
  • 1.5 Tractability frontiers (for CSPs)
  • 1.6 Conclusion
  • References
  • 2 Perfect Graphs and Graphical Modeling
  • 2.1 Berge Graphs and Perfect Graphs
  • 2.2 Computational Properties of Perfect Graphs
  • 2.3 Graphical Models
  • 2.4 Nand Markov Random Fields
  • 2.5 Maximum Weight Stable Set2.6 Tractable Graphical Models
  • 2.7 Discussion
  • 2.8 Acknowledgments
  • 2.9 Appendix
  • References
  • Part 2: Language Restrictions
  • 3 Submodular Function Maximization
  • 3.1 Submodular Functions
  • 3.2 Greedy Maximization of Submodular Functions
  • 3.3 Beyond the Greedy Algorithm: Handling More Complex Constraints
  • 3.4 Online Maximization of Submodular Functions
  • 3.5 Adaptive Submodularity
  • 3.6 Conclusions
  • References
  • 4 Tractable Valued Constraints
  • 4.1 Introduction
  • 4.2 Constraint Satisfaction Problems
  • 4.3 Valued Constraint Satisfaction Problems4.4 Examples of Valued Constraint Languages
  • 4.5 Expressive Power
  • 4.6 Submodular Functions and Multimorphisms
  • 4.7 Conservative Valued Constraint Languages
  • 4.8 A General Algebraic Theory of Complexity
  • 4.9 Conclusions and Open Problems
  • References
  • 5 Tractable Knowledge Representation Formalisms
  • 5.1 Introduction
  • 5.2 A Motivating Example
  • 5.3 Negation Normal Form
  • 5.4 Structured Decomposability
  • 5.5 (X, Y)-Decompositions of Boolean Functions
  • 5.6 Sentential Decision Diagrams
  • 5.7 The Process of Compilation5.8 Knowledge Compilation in Probabilistic Reasoning
  • 5.9 Conclusion
  • References
  • Part 3: Algorithms and their Analysis
  • 6 Tree-Reweighted Message Passing
  • 6.1 Introduction
  • 6.2 Preliminaries
  • 6.3 Sequential Tree-Reweighted Message Passing (TRW-S)
  • 6.4 Analysis of the Algorithm
  • 6.5 TRW-S with Monotonic Chains
  • 6.6 Summary of the TRW-S Algorithm
  • 6.7 Related Approaches
  • 6.8 Conclusions and Discussion
  • References
  • 7 Tractable Optimization in Machine Learning
  • 7.1 Introduction
  • 7.2 Background
  • 7.3 Smooth Convex Optimization7.4 Nonsmooth Convex Optimization
  • 7.5 Stochastic Optimization
  • 7.6 Summary
  • References
  • 8 Approximation Algorithms
  • 8.1 Introduction
  • 8.2 Combinatorial Algorithms
  • 8.3 Linear Programming Based Algorithms
  • 8.4 Semi-Definite Programming Based Algorithms
  • 8.5 Algorithms for Special Instances
  • 8.6 Metric Embeddings
  • 8.7 Hardness of Approximation
  • References
  • 9 Kernelization Methods for Fixed-Parameter Tractability
  • 9.1 Introduction
  • 9.2 Basic Definitions
  • 9.3 Classical Techniques