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Probability Theory and Combinatorial Optimization by J. Michael Steele (Paperback, 1987)

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This monograph provides an introduction to the state of the art of the probability theory that is most directly applicable to combinatorial optimization. Much attention is paid to those questions dealing with discrete optimization problems for points in Euclidean space, such as the minimum spanning tree, the travelling-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. There are three fundamental probabilistic themes that are examined through our concrete investigations. First, there is a systematic exploration of martingales. Many investigators of problems of combinatorial optimization have come to count on martingale inequalities as versatile tools which let us show that many of the naturally occurring random variables of combinatorial optimization are sharply concentrated about their means - a phenomenon with numerous practical and theoretical consequences. The second theme that is explored is the systematic use of subadditivity of several flavours, ranging from the naive subadditivity of real sequences to the subtler subadditivity of stochastic processes. By and large, subadditivity offers only elementary tools, but on remarkably many occasions such tools provide the key organizing principle in the attack on problems of nearly intractable difficulty. The third and deepest theme developed here concerns the application of Talagrand's isoperimetric theory of concentration inequalities which has affected much that is known in the probability theory of combinatorial optimization. The treatment given here deals with only a small part of Talagrand's theory, but the reader should find considerable coaching on how to use some of the most important ideas from that theory.

Product Identifiers

Publisher
Society for Industrial & Applied Mathematics,U.S.
ISBN-13
9780898713800
eBay Product ID (ePID)
96701243

Product Key Features

Author
J. Michael Steele
Publication Name
Probability Theory and Combinatorial Optimization
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
1987
Type
Textbook
Number of Pages
167 Pages

Dimensions

Item Height
250mm
Item Width
177mm
Item Weight
304g

Additional Product Features

Title_Author
J. Michael Steele
Series Title
Cbms-Nsf Regional Conference Series in Applied Mathematics
Country/Region of Manufacture
United States

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Probability Theory and Combinatorial Optimization by J. Michael Steele (Paperback, 1987)

About this product

Product Information

Product Identifiers

Product Key Features

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Additional Product Features

Best Selling in Adult Learning & University

The Weed Forager's Handbook: A Guide to Edible and Medicinal Weeds in Australia by Adam Grubb, Annie Raser-Rowland (2012, Paperback)

Australian Native Bee Book: Keeping Stingless Bee Hives for Pets, Pollination and Sugarbag Honey by Tim Heard (Paperback, 2015)

The Falsification of History: Our Distorted Reality by John Hamer (Paperback, 2013)

Permaculture: A Designer's Manual by Bill Mollison (Hardcover, 1988)

In-Basket Case Studies by Guy Adamson (Paperback, 1986)

Empire of the Summer Moon: Quanah Parker and the Rise and Fall of the Comanches, the Most Powerful Indian Tribe in American History by S.C. Gwynne (Paperback, 2011)

Botanical Field Guide by Stefan Mager (Fold-out book or chart, 2021)

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Sally Fallon Morell Thomas S. Cowan The Contagion Myth (Hardback) (US IMPORT)

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