Recent Advances in Algorithms and Combinatorics

1. Front Matter

   Pages i-xiii

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2. The Matching Lattice

   • M. H. de Carvalho, C. L. Lucchesi, U. S. R. Murty

   Pages 1-25

3. Discrete Mathematics and Radio Channel Assignment

   • C. McDiarmid

   Pages 27-63

4. On the coloration of perfect graphs

   • F. Maffray

   Pages 65-84

5. Algorithmic Aspects of Tree Width

   • B. A. Reed

   Pages 85-107

6. A Survey on Clique Graphs

   • J. L. Szwarcfiter

   Pages 109-136

7. Semidefinite Programs and Combinatorial Optimization

   • L. Lovász

   Pages 137-194

8. Approximability of NP-Optimization Problems

   • A. Steger

   Pages 195-243

9. Pattern Inference under many Guises

   • M.-F. Sagot, Y. Wakabayashi

   Pages 245-287

10. Szemerédi’s Regularity Lemma and Quasi-randomness

    • Y. Kohayakawa, V. Rödl

    Pages 289-351

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.

• Algorithmic Combinatorics
• Algorithms in Graph Theory
• Graph
• Graph theory
• Matching
• Theory of Algorithms
• algorithms
• combinatorics
• algorithm analysis and problem complexity

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)

• Equipe Combinatoire, CNRS, Paris, France

  Bruce A. Reed

• McGill University, Montreal, Canada

  Bruce A. Reed

• Departamento de Computacao—LIA, Universidade Federal do Ceara, Fortaleza, Brasil

  Cláudia L. Sales

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