Sequences and the de Bruijn Graph

Properties, Constructions, and Applications

Tuvi Etzion

• Publisher: Academic Press
• Year: 2024
• Print ISBN:
  9780443135170
• eBook ISBN:
  9780443135187
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

The de Bruijn graph was defined in 1949 to enumerate the number of closed sequences where each n-tuple appears exactly once as a window in a sequence. Through the years, the graph and its sequences have found numerous applications – in space technology, wireless communication, cryptography, parallel computation, genome assembly, DNA storage, and microbiome research, among others. Sequences and the de Bruijn Graph: Properties, Constructions, and Applications explores the foundations of theoretical mathematical concepts and the important applications to computer science, electrical engineering, and bioinformatics. The book introduces the various concepts, ideas, and techniques associated with the use of the de Bruijn Graph, providing comprehensive coverage of sequence classification, one-dimensional and two-dimensional applications, graphs, interconnected networks, layouts, and embedded systems. Researchers, graduate students, professors, and professionals working in the fields of applied mathematics, electrical engineering, computer science and bioinformatics will find this book useful. - Investigates computational and engineering applications associated with the de Bruijn graph, its sequences, and their generalization - Explores one-dimensional and two-dimensional sequences with special properties and their various properties and applications - Introduces the rich structure of the de Bruijn graph and its sequences, in both mathematical theory and its applications to computing and engineering problems

Table of contents

• Cover
• Front Matter
• Table of Contents
• Copyright
• Dedication
• Contents
• Preface
• List of Illustrations
• List of Tables
• Chapter 1 : Introduction: Preliminaries, de Bruijn graph, shift registers
• Chapter 2 : LFSR sequences: Polynomials, M-sequences, cycles, difference sets
• Chapter 3 : Cycles and the nonlinear theory: Necklaces, self-dual sequences, enumeration
• Chapter 4 : Constructions of full cycles: Full cycles, enumeration, D-morphism, algorithms
• Chapter 5 : Linear complexity of sequences: Algorithms, complexity of de Bruijn sequences
• Chapter 6 : Classification of sequences: Balanced sequences, the depth of a sequence
• Chapter 7 : One-dimensional applications: Cryptography, verification, Gray codes, and games
• Chapter 8 : DNA sequences and DNA codes: The genome assembly and DNA storage
• Chapter 9 : Two-dimensional arrays: Perfect maps and distinct differences arrays
• Chapter 10 : Two-dimensional applications: Self-location, secure sensor networks, folding
• Chapter 11 : Unique path property graphs: Properties, constructions, cycles, and factors
• Chapter 12 : Interconnection networks: Shuffle-exchange and permutation networks, layouts
• Index
• Symbols