Probabilistic Methods for Algorithmic Discrete Mathematics

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.

Inhaltsverzeichnis

The Probabilistic Method.- Probabilistic Analysis of Algorithms.- An Overview of Randomized Algorithms.- Mathematical Foundations of the Markov Chain Monte Carlo Method.- Percolation and the Random Cluster Model: Combinatorial and Algorithmic Problems.- Concentration.- Branching Processes and Their Applications in the Analysis of Tree Structures and Tree Algorithms.- Author Index.

Produktdetails

• Mitarbeit: Michel Habib (Herausgeber), Coli McDiarmid (Herausgeber), Colin McDiarmid (Herausgeber), Jorge Ramirez-Alfonsin (Herausgeber), Jorge Ramirez-Alfonsin et al (Herausgeber), Bruce Reed (Herausgeber)
• Verlag: Springer, Berlin
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 01.07.2009
• EAN: 9783540646228
• ISBN: 978-3-540-64622-8
• Seiten: 325
• Abmessung: 155 mm x 235 mm x 23 mm
• Gewicht: 678 g
• Illustration: XVII, 325 p.
• Serien: Algorithms and Combinatorics; Algorithms and Combinatorics, Volume 16; Algorithms and Combinatorics
• Themen: Kinder- und Jugendbücher > Jugendbücher ab 12 Jahre; Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik