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The Complexity of Valued Constraint Satisfaction Problems: Cognitive Technologies

Autor Stanislav Živný
en Limba Engleză Paperback – 9 noi 2014
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.
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Specificații

ISBN-13: 9783642434563
ISBN-10: 3642434568
Pagini: 188
Ilustrații: XVIII, 170 p.
Dimensiuni: 155 x 235 x 10 mm
Greutate: 0.27 kg
Ediția:2012
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Cognitive Technologies

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

Chap. 1 Introduction.- Chap. 2 Background.- Chap. 3 Expressibility of Valued Constraints.- Chap. 4 Expressibility of Fixed-Arity Languages.- Chap. 5 Expressibility of Submodular Languages.- Chap. 6 Non-expressibility of Submodular Languages.- Chap. 7 Tractable Languages.- Chap. 8  Conservative Languages.- Chap. 9 The Power of Linear Programming.- Chap. 10 Hybrid Tractability.- Chap. 11 Summary and Open Problems.- References.- Index.

Recenzii

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)

Notă biografică

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.

Textul de pe ultima copertă

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.

Caracteristici

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