โ Scribed by Stanislav ลฝivnรฝ (auth.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages I-XVII
Front Matter....Pages 1-1
Background....Pages 3-27
Front Matter....Pages 29-29
Expressibility of Valued Constraints....Pages 31-47
Expressibility of Fixed-Arity Languages....Pages 49-78
Expressibility of Submodular Languages....Pages 79-94
Non-expressibility of Submodular Languages....Pages 95-114
Front Matter....Pages 115-115
Tractable Languages....Pages 117-124
Conservative Languages....Pages 125-129
The Power of Linear Programming....Pages 131-135
Hybrid Tractability....Pages 137-149
Summary and Open Problems....Pages 151-152
Back Matter....Pages 153-170
Theory of Computation; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Mathematics of Computing
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