Probability Theory and Combinatorial Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability Theory and Combinatorial Optimization write by J. Michael Steele. This book was released on 1997-01-01. Probability Theory and Combinatorial Optimization available in PDF, EPUB and Kindle. 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.
Probability Theory of Classical Euclidean Optimization Problems
Probability Theory of Classical Euclidean Optimization Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability Theory of Classical Euclidean Optimization Problems write by Joseph E. Yukich. This book was released on 2006-11-14. Probability Theory of Classical Euclidean Optimization Problems available in PDF, EPUB and Kindle. 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.
Handbook of Combinatorial Optimization and Probability Theory
Handbook of Combinatorial Optimization and Probability Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Combinatorial Optimization and Probability Theory write by Louisa A. May. This book was released on 2012-09. Handbook of Combinatorial Optimization and Probability Theory available in PDF, EPUB and Kindle. This handbook provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization, with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the traveling-salesman tour, and minimal-length matchings. 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.
Handbook of combinatorial optimization & probability theory
Handbook of combinatorial optimization & probability theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of combinatorial optimization & probability theory write by . This book was released on 2016. Handbook of combinatorial optimization & probability theory available in PDF, EPUB and Kindle.
Handbook of Combinatorial Optimization
Handbook of Combinatorial Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Combinatorial Optimization write by Ding-Zhu Du. This book was released on 2013-03-14. Handbook of Combinatorial Optimization available in PDF, EPUB and Kindle. Combinatorial (or discrete) optimization is one of the most active fields in the interface of operations research, computer science, and applied math ematics. Combinatorial optimization problems arise in various applications, including communications network design, VLSI design, machine vision, air line crew scheduling, corporate planning, computer-aided design and man ufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. Furthermore, combinatorial optimization problems occur in many diverse areas such as linear and integer programming, graph theory, artificial intelligence, and number theory. All these problems, when formulated mathematically as the minimization or maximization of a certain function defined on some domain, have a commonality of discreteness. Historically, combinatorial optimization starts with linear programming. Linear programming has an entire range of important applications including production planning and distribution, personnel assignment, finance, alloca tion of economic resources, circuit simulation, and control systems. Leonid Kantorovich and Tjalling Koopmans received the Nobel Prize (1975) for their work on the optimal allocation of resources. Two important discover ies, the ellipsoid method (1979) and interior point approaches (1984) both provide polynomial time algorithms for linear programming. These algo rithms have had a profound effect in combinatorial optimization. Many polynomial-time solvable combinatorial optimization problems are special cases of linear programming (e.g. matching and maximum flow). In addi tion, linear programming relaxations are often the basis for many approxi mation algorithms for solving NP-hard problems (e.g. dual heuristics).
