Authors:
- Presents general methods for analysing the complexity of optimisation problems cast as valued constraint satisfaction problems (VCSPs)
- Suitable for researchers interested in methods and results from the area of constraint programming and discrete optimisation
- Related thesis received ACP (Association for Constraint Programming) Doctoral Award
- Includes supplementary material: sn.pub/extras
Part of the book series: Cognitive Technologies (COGTECH)
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Table of contents (10 chapters)
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Front Matter
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Background
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Front Matter
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Part I
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Tractability
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Front Matter
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Back Matter
About this book
The topic of this book is the following optimisation problem: given a set of discrete variables and a set of functions, each depending on a subset of the variables, minimise the sum of the functions over all variables. This fundamental research problem has been studied within several different contexts of discrete mathematics, computer science and artificial intelligence under different names: Min-Sum problems, MAP inference in Markov random fields (MRFs) and conditional random fields (CRFs), Gibbs energy minimisation, valued constraint satisfaction problems (VCSPs), and, for two-state variables, pseudo-Boolean optimisation.
In this book the author presents general techniques for analysing the structure of such functions and the computational complexity of the minimisation problem, and he gives a comprehensive list of tractable cases. Moreover, he demonstrates that the so-called algebraic approach to VCSPs can be used not only for the search for tractable VCSPs, but also for other questions such as finding the boundaries to the applicability of certain algorithmic techniques.
The book is suitable for researchers interested in methods and results from the area of constraint programming and discrete optimisation.
Reviews
From the reviews:
“The book is concerned with valued constraint satisfaction problems with finite domains, i. e., the problem of minimising the sum of functions that each depend on some subset of a finite set of discrete variables with finite domains. … In all places the description is very precise and exact, detailed where needed. This makes it a very useful reference for researchers working in the field.” (Thomas Jansen, zbMATH, Vol. 1283, 2014)
Authors and Affiliations
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University College, University of Oxford, Oxford, United Kingdom
Stanislav Živný
About the author
Bibliographic Information
Book Title: The Complexity of Valued Constraint Satisfaction Problems
Authors: Stanislav Živný
Series Title: Cognitive Technologies
DOI: https://doi.org/10.1007/978-3-642-33974-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2012
Hardcover ISBN: 978-3-642-33973-8Published: 20 October 2012
Softcover ISBN: 978-3-642-43456-3Published: 09 November 2014
eBook ISBN: 978-3-642-33974-5Published: 19 October 2012
Series ISSN: 1611-2482
Series E-ISSN: 2197-6635
Edition Number: 1
Number of Pages: XVIII, 170
Topics: Theory of Computation, Artificial Intelligence, Mathematical Logic and Foundations, Mathematics of Computing
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