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Probabilistic Methods for Algorithmic Discrete Mathematics : Algorithms and Combinatorics - Michel Habib

Probabilistic Methods for Algorithmic Discrete Mathematics

Algorithms and Combinatorics

By: Michel Habib (Editor), Colin McDiarmid (Editor), Jorge L. Ramirez Alfonsin (Editor), Bruce Reed (Editor)

Hardcover Published: 19th August 1998
ISBN: 9783540646228
Number Of Pages: 325

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Leave nothing to chance. This cliche embodies the common belief that ran­ domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba­ bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus­ sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech­ niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

The Probabilistic Methodp. 1
Probabilistic Analysis of Algorithmsp. 36
An Overview of Randomized Algorithmsp. 93
Mathematical Foundations of the Markov Chain Monte Carlo Methodp. 116
Percolation and the Random Cluster Model: Combinatorial and Algorithmic Problemsp. 166
Concentrationp. 195
Branching Processes and Their Applications in the Analysis of Tree Structures and Tree Algorithmsp. 249
Author Indexp. 315
Subject Indexp. 321
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540646228
ISBN-10: 3540646221
Series: Algorithms and Combinatorics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 325
Published: 19th August 1998
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.4 x 15.6  x 2.54
Weight (kg): 0.66