The Complexity of Valued Constraint Satisfaction Problems

  • Stanislav Živný

Part of the Cognitive Technologies book series (COGTECH)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Background

    1. Front Matter
      Pages 1-1
    2. Stanislav Živný
      Pages 3-27
  3. Expressive Power

    1. Front Matter
      Pages 29-29
    2. Stanislav Živný
      Pages 31-47
    3. Stanislav Živný
      Pages 49-78
    4. Stanislav Živný
      Pages 79-94
    5. Stanislav Živný
      Pages 95-114
  4. Tractability

    1. Front Matter
      Pages 115-115
    2. Stanislav Živný
      Pages 117-124
    3. Stanislav Živný
      Pages 125-129
    4. Stanislav Živný
      Pages 131-135
    5. Stanislav Živný
      Pages 137-149
    6. Stanislav Živný
      Pages 151-152
  5. Back Matter
    Pages 153-170

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.


Algorithms Constraint programming (CP) Constraint satisfaction problem (CSP) Discrete optimization Linear programming (LP) Tractability Tractable languages Valued Constraint satisfaction problems (VCSPs)

Authors and affiliations

  • Stanislav Živný
    • 1
  1. 1.University CollegeUniversity of OxfordOxfordUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Computer Science
  • Print ISBN 978-3-642-33973-8
  • Online ISBN 978-3-642-33974-5
  • Series Print ISSN 1611-2482
  • Buy this book on publisher's site