Guide to Graph Colouring: Algorithms and Applications

ISBN-13: 9783030810566 / Angielski / Miękka / 2022

R. M. R. Lewis

Opis

This textbook treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, complexity theory,  bounds and constructive algorithms. The author then shows how advanced, graph colouring techniques can be applied to classic real-world operational research problems such as designing seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by an online suite of downloadable code. The book is of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.

Spis treści

1. Introduction to Graph Colouring.- 2. Bounds and Constructive Algorithms.- 3. Advanced Techniques for Graph Colouring.- 4. Algorithm Case Studies.- 5. Applications and Extensions.- 6. Designing Seating Plans.- 7. Designing Sports Leagues.- 8. Designing University Timetables.

O autorze

Dr. Rhyd Lewis is a reader in operational research at Cardiff School of Mathematics, Cardiff University. Previously, he was a lecturer in quantitative methods at Cardiff Business School. He holds a Ph.D. in Computer Science and Operational Research from Edinburgh Napier University. His research interests cover algorithmic graph theory and the analysis and application of metaheuristic algorithms. He is a cofounder and associate editor of the Intl. J. of Metaheuristics.

Blurb

This unique textbook treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. 

The work describes and analyses some of the best-known algorithms for colouring graphs, focusing on:  whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. 

Introductory chapters explain graph colouring, complexity theory, bounds and constructive algorithms. Further exposition then shows how advanced graph-colouring techniques can be applied to classic real-world operational research problems, such as designing seating plans, sports scheduling, and university timetabling.  Readers should have elementary knowledge of sets, matrices, and enumerative combinatorics.

Topics and features:

• Suitable for graduate or upper-undergraduate courses in computer science, operations research, mathematics, and engineering
• Focuses on state-of-the-art algorithmic solutions to classic, real-world problems
• Supported by online suite of downloadable code
• Includes many examples, suggestions for further reading, and historical notes

This fine new edition will be of real value to graduate students, researchers, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence.  It thus will fulfill a dual role as both a key textbook for academia and a guidebook for professional self-study and pursuits.

Dr. Rhyd Lewis is a reader in operational research at Cardiff School of Mathematics, Cardiff University, UK. Previously he was a lecturer in quantitative methods at Cardiff Business School.