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Recent Advances in Algorithms and Combinatorics: CMS Books in Mathematics

Editat de Bruce A. Reed, Claudia L. Linhares-Sales
en Limba Engleză Hardback – 22 noi 2002
Combinatorics is one of the fastest growing ?elds of mathematics. In large measure this is because many practical problems can be modeled and then e?ciently solved using combinatorial theory. This real world motivation for studying algorithmic combinatorics has led not only to the development of many software packages but also to some beautiful mathematics which has nodirectapplicationtoappliedproblems. Inthisvolumewehighlightsome exciting recent developments in algorithmic combinatorics. Most practical applications of algorithmic combinatorics would be - possible without the use of the computer. As computers become ever more powerful, more and more applications become possible. Computational biology is one example of a relatively new ?eld in which algorithmic c- binatorics plays a key role. The chapter by Sagot and Wakabayashi in this volumediscusseshowcombinatorialtoolscanbeusedtosearchforpatterns in DNA and protein sequences. The information technology revolution has not only allowed for the r- olution of practical problems using combinatorial techniques, it has also been the source of many new combinatorial problems. One example is - dio channel assignment. In this problem we have a number of transmitters each of which must handle a number of calls. Each call must be assigned a frequency in such a way that interference is avoided (thus calls handled by the same transmitter are assigned di?erent frequencies as are calls handled by transmitters which are near each other). The explosive growth in the use of the frequency spectrum due to, e. g. , mobile telephone networks, has made it a very valuable resource.
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Specificații

ISBN-13: 9780387954349
ISBN-10: 0387954341
Pagini: 352
Ilustrații: XIV, 352 p.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.64 kg
Ediția:2003
Editura: Springer
Colecția Springer
Seria CMS Books in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

The Matching Lattice.- Discrete Mathematics and Radio Channel Assignment.- On the coloration of perfect graphs.- Algorithmic Aspects of Tree Width.- A Survey on Clique Graphs.- Semidefinite Programs and Combinatorial Optimization.- Approximability of NP-Optimization Problems.- Pattern Inference under many Guises.- Szemerédi’s Regularity Lemma and Quasi-randomness.

Recenzii

From the reviews:
"Combinatorics is one of the fastest growing fields of mathematics. … From the table of contents one can see the wide range of topics covered. The authors are acknowledged researchers of the presented fields and guarantee the high quality of the volume. If you want to be up-to-date in combinatorics you should have this volume close to your hands." (Péter Hajnal, Acta Scientarium Mathematicarum, Vol. 69, 2003)
"This edited volume contains nine carefully written chapters in the area of combinatorics. … The book is very well written and can be read individually by research students. The volume is of definite interest for researchers in combinatorics, graph theory and theoretical computer science. This book is certainly value for money and I would highly recommend it as an essential purchase for a university library." (G. Gutin, Journal of the Operational Research Society, Vol. 55 (5), 2004)

Textul de pe ultima copertă

Combinatorics is one of the fastest growing fields of mathematics. One reason for this is because many practical problems can be modeled and then efficiently solved using combinatorial theory. This real world motivation for studying algorithmic combinatorics has led not only to the development of many software packages but also to some beautiful mathematics which has no direct application to applied problems. This book highlights a few of the exciting recent developments in algorithmic combinatorics, including the search for patterns in DNA and protein sequences, the theory of semi-definite programming and its role in combinatorial optimization, and the algorithmic aspects of tree decompositions and it's applications to the theory of databases, code optimization, and bioinformatics.

Claudia Linhares-Sales is Assistant Professor of Computer Science at the Federal University of Cear, Brazil. Bruce Reed is Canada Research Chair in Graph Theory at the School of Computer Science of McGill Univeristy.