Cognitive Technologies

The Complexity of Valued Constraint Satisfaction Problems

Authors: Zivny, Stanislav

  • 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
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  • ISBN 978-3-642-33974-5
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Hardcover $139.00
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  • ISBN 978-3-642-33973-8
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Softcover $139.00
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  • ISBN 978-3-642-43456-3
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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.

About the authors

Dr. Stanislav Živný has a Ph.D. in Computer Science from the University of Oxford, and he was a Junior Research Fellow in Mathematical and Physical Sciences at Oxford's University College. The doctoral thesis won the 2011 ACP (Association for Constraint Programming) Doctoral Award for the best thesis in the area of constraint programming from the previous two years. He was awarded a Senior Research Fellowship in Advances in Discrete Mathematics and its Applications, hosted by the University of Warwick, which commenced in autumn 2012.

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)


Table of contents (10 chapters)

  • Background

    Živný, Stanislav

    Pages 3-27

  • Expressibility of Valued Constraints

    Živný, Stanislav

    Pages 31-47

  • Expressibility of Fixed-Arity Languages

    Živný, Stanislav

    Pages 49-78

  • Expressibility of Submodular Languages

    Živný, Stanislav

    Pages 79-94

  • Non-expressibility of Submodular Languages

    Živný, Stanislav

    Pages 95-114

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-642-33974-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-642-33973-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-642-43456-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Complexity of Valued Constraint Satisfaction Problems
Authors
Series Title
Cognitive Technologies
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-33974-5
DOI
10.1007/978-3-642-33974-5
Hardcover ISBN
978-3-642-33973-8
Softcover ISBN
978-3-642-43456-3
Series ISSN
1611-2482
Edition Number
1
Number of Pages
XVIII, 170
Topics