Finite Markov Chains And Algorithmic Applications
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Finite Markov Chains and Algorithmic Applications
Author: Olle Häggström
language: en
Publisher: Cambridge University Press
Release Date: 2002-05-30
Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.
Algorithms for Random Generation and Counting: A Markov Chain Approach
Author: A. Sinclair
language: en
Publisher: Springer Science & Business Media
Release Date: 1993-02
This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.
General Irreducible Markov Chains and Non-Negative Operators
Author: Esa Nummelin
language: en
Publisher: Cambridge University Press
Release Date: 2004-06-03
Presents the theory of general irreducible Markov chains and its connection to the Perron-Frobenius theory of nonnegative operators.