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Probabilistic Combinatorial Optimization on Graphsby Cécile Murat; Vangelis Th. Paschos
ISTE 2006; US$ 92.00This title provides a comprehensive survey over the subject of probabilistic combinatorial optimization, discussing probabilistic versions of some of the most paradigmatic combinatorial problems on graphs, such as the maximum independent set, the minimum vertex covering, the longest path and the minimum coloring. Detailed discussion is given to a priori optimization, which is adopted as the main working hypothesis: starting from an a priori solution of a ?super instance? of a problem, where any datum is present with a certain probability, this hypothesis consists of creating modifications in order to fit the real instance to be optimized: that is, a sub-instance of the super instance. The main objective of the a priori optimization is the... more...
Probabilistic Combinatorial Optimization on Graphsby Cé Murat; cile; Vangelis Th. Paschos
John Wiley & Sons 2010; US$ 125.00This title provides a comprehensive survey over the subject of probabilistic combinatorial optimization, discussing probabilistic versions of some of the most paradigmatic combinatorial problems on graphs, such as the maximum independent set, the minimum vertex covering, the longest path and the minimum coloring. Those who possess a sound knowledge of the subject mater will find the title of great interest, but those who have only some mathematical familiarity and knowledge about complexity and approximation theory will also find it an accessible and informative read. more...
Random Walks, Boundaries and Spectraby Daniel Lenz; Florian Sobieczky; Wolfgang Woess
Springer 2011; US$ 149.00These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'. more...
Towards Intelligent Modelingby George A. Anastassiou; Oktay Duman
Springer 2011; US$ 129.00The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present... more...
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