UID:
almahu_9948234319902882
Format:
1 online resource (xxi, 377 pages) :
,
digital, PDF file(s).
ISBN:
9781139177801 (ebook)
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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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 Set; 2.6 Tractable Graphical Models; 2.7 Discussion.
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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 Problems; 4.4 Examples of Valued Constraint Languages; 4.5 Expressive Power.
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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 Compilation; 5.8 Knowledge Compilation in Probabilistic Reasoning; 5.9 Conclusion; References; Part 3: Algorithms and their Analysis.
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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 Optimization; 7.4 Nonsmooth Convex Optimization; 7.5 Stochastic Optimization; 7.6 Summary; References; 8 Approximation Algorithms; 8.1 Introduction; 8.2 Combinatorial Algorithms.
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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; 9.4 Recent Upper Bound Machinery; 9.5 Conclusion; References; Part 4: Tractability in Some Specific Areas; 10 Efficient Submodular Function Minimization for Computer Vision; 10.1 Labeling Problems in Computer Vision; 10.2 Markov and Conditional Random Fields; 10.3 Minimizing Energy Functions for MAP Inference.
Additional Edition:
Print version: ISBN 9781107025196
Language:
English
URL:
https://doi.org/10.1017/CBO9781139177801
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