Probability Theory and Combinatorial Optimization PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Probability Theory and Combinatorial Optimization PDF full book. Access full book title Probability Theory and Combinatorial Optimization by J. Michael Steele. Download full books in PDF and EPUB format.
Author: J. Michael Steele
Publisher: SIAM
ISBN: 9781611970029
Category : Mathematics
Languages : en
Pages : 168
Get Book Here
Book Description
This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles. There are three fundamental probabilistic themes that are examined through our concrete investigations. First, there is a systematic exploitation of martingales. The second theme that is explored is the systematic use of subadditivity of several flavors, ranging from the naïve subadditivity of real sequences to the subtler subadditivity of stochastic processes. The third and deepest theme developed here concerns the application of Talagrand's isoperimetric theory of concentration inequalities.
Author: J. Michael Steele
Publisher: SIAM
ISBN: 9781611970029
Category : Mathematics
Languages : en
Pages : 168
Get Book Here
Book Description
This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. Still, there are several nongeometric optimization problems that receive full treatment, and these include the problems of the longest common subsequence and the longest increasing subsequence. The philosophy that guides the exposition is that analysis of concrete problems is the most effective way to explain even the most general methods or abstract principles. There are three fundamental probabilistic themes that are examined through our concrete investigations. First, there is a systematic exploitation of martingales. The second theme that is explored is the systematic use of subadditivity of several flavors, ranging from the naïve subadditivity of real sequences to the subtler subadditivity of stochastic processes. The third and deepest theme developed here concerns the application of Talagrand's isoperimetric theory of concentration inequalities.
Author: J. Michael Steele
Publisher: SIAM
ISBN: 0898713803
Category : Mathematics
Languages : en
Pages : 164
Get Book Here
Book Description
An introduction to the state of the art of the probability theory most applicable to combinatorial optimization. The questions that receive the most attention are those that deal with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings.
Author: Martin Grötschel
Publisher: Springer Science & Business Media
ISBN: 3642978819
Category : Mathematics
Languages : en
Pages : 374
Get Book Here
Book Description
Historically, there is a close connection between geometry and optImization. This is illustrated by methods like the gradient method and the simplex method, which are associated with clear geometric pictures. In combinatorial optimization, however, many of the strongest and most frequently used algorithms are based on the discrete structure of the problems: the greedy algorithm, shortest path and alternating path methods, branch-and-bound, etc. In the last several years geometric methods, in particular polyhedral combinatorics, have played a more and more profound role in combinatorial optimization as well. Our book discusses two recent geometric algorithms that have turned out to have particularly interesting consequences in combinatorial optimization, at least from a theoretical point of view. These algorithms are able to utilize the rich body of results in polyhedral combinatorics. The first of these algorithms is the ellipsoid method, developed for nonlinear programming by N. Z. Shor, D. B. Yudin, and A. S. NemirovskiI. It was a great surprise when L. G. Khachiyan showed that this method can be adapted to solve linear programs in polynomial time, thus solving an important open theoretical problem. While the ellipsoid method has not proved to be competitive with the simplex method in practice, it does have some features which make it particularly suited for the purposes of combinatorial optimization. The second algorithm we discuss finds its roots in the classical "geometry of numbers", developed by Minkowski. This method has had traditionally deep applications in number theory, in particular in diophantine approximation.
Author: Jon Lee
Publisher: Cambridge University Press
ISBN: 9780521010122
Category : Business & Economics
Languages : en
Pages : 232
Get Book Here
Book Description
A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.
Author: Joseph E. Yukich
Publisher: Springer
ISBN: 354069627X
Category : Mathematics
Languages : en
Pages : 162
Get Book Here
Book Description
This monograph describes the stochastic behavior of the solutions to the classic problems of Euclidean combinatorial optimization, computational geometry, and operations research. Using two-sided additivity and isoperimetry, it formulates general methods describing the total edge length of random graphs in Euclidean space. The approach furnishes strong laws of large numbers, large deviations, and rates of convergence for solutions to the random versions of various classic optimization problems, including the traveling salesman, minimal spanning tree, minimal matching, minimal triangulation, two-factor, and k-median problems. Essentially self-contained, this monograph may be read by probabilists, combinatorialists, graph theorists, and theoretical computer scientists.
Author: J. M. Cushing
Publisher: SIAM
ISBN: 0898714176
Category : Science
Languages : en
Pages : 204
Get Book Here
Book Description
This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models.
Author: Harry Kesten
Publisher: Springer
ISBN: 9783662094457
Category : Mathematics
Languages : en
Pages : 351
Get Book Here
Book Description
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
Author: Gerard Cornuejols
Publisher: SIAM
ISBN: 0898714818
Category : Mathematics
Languages : en
Pages : 140
Get Book Here
Book Description
New and elegant proofs of classical results and makes difficult results accessible.
Author: Anne Auger
Publisher: World Scientific
ISBN: 9814282669
Category : Computers
Languages : en
Pages : 370
Get Book Here
Book Description
This volume covers both classical results and the most recent theoretical developments in the field of randomized search heuristics such as runtime analysis, drift analysis and convergence.
Author: Jinho Baik
Publisher: American Mathematical Soc.
ISBN: 0821848410
Category : Mathematics
Languages : en
Pages : 478
Get Book Here
Book Description
Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.
