Probabilistic Methods for Algorithmic Discrete Mathematics

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Synopsis

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.

Book details

Edition:
1998
Series:
Algorithms and Combinatorics (Book 16)
Author:
Michel Habib, Colin McDiarmid, Jorge Ramirez-Alfonsin, Bruce Reed
ISBN:
9783662127889
Related ISBNs:
9783540646228
Publisher:
Springer Berlin Heidelberg
Pages:
N/A
Reading age:
Not specified
Includes images:
No
Date of addition:
2022-07-14
Usage restrictions:
Copyright
Copyright date:
1998
Copyright by:
N/A 
Adult content:
No
Language:
English
Categories:
Computers and Internet, Mathematics and Statistics, Nonfiction