|
Showing 1 - 3 of
3 matches in All Departments
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 book gives an accessible account of modern probabilistic methods for analyzing combinatorial structures and algorithms. It will be an useful guide for graduate students and researchers.Special features included: a simple treatment of Talagrand's inequalities and their applications; an overview and many carefully worked out examples of the probabilistic analysis of combinatorial algorithms; a discussion of the "exact simulation" algorithm (in the context of Markov Chain Monte Carlo Methods); a general method for finding asymptotically optimal or near optimal graph colouring, showing how the probabilistic method may be fine-tuned to exploit the structure of the underlying graph; a succinct treatment of randomized algorithms and derandomization techniques.
The theory of random graphs is a vital part of the education of any
researcher entering the fascinating world of combinatorics.
However, due to their diverse nature, the geometric and structural
aspects of the theory often remain an obscure part of the formative
study of young combinatorialists and probabilists. Moreover, the
theory itself, even in its most basic forms, is often considered
too advanced to be part of undergraduate curricula, and those who
are interested usually learn it mostly through self-study, covering
a lot of its fundamentals but little of the more recent
developments. This book provides a self-contained and concise
introduction to recent developments and techniques for classical
problems in the theory of random graphs. Moreover, it covers
geometric and topological aspects of the theory and introduces the
reader to the diversity and depth of the methods that have been
devised in this context.
|
You may like...
Caracal
Disclosure
CD
R50
Discovery Miles 500
|