Sequences and the de Bruijn Graph: Properties, Constructions, and Applications explores the foundations of theoretical mathematical concepts and their 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 properties, constructions, and interconnection networks. This book is suitable for researchers, graduate students, professors, and professionals working in the fields of applied mathematics, electrical engineering, computer science, and bioinformatics. The de Bruijn graph was defined in 1946 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.
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Table of Contents
1. Introduction2. LFSR sequences
3. Cycles and the nonlinear theory
4. Constructions of full cycles
5. Linear complexity of sequences
6. Classification of sequences
7. One-dimensional applications
8. DNA sequences and DNA codes
9. Two-dimensional arrays
10. Two-dimensional applications
11. Unique path property graphs
12. Interconnection networks
Authors
Tuvi Etzion Professor, Technion - Israel Institute of Technology, Haifa, Israel.Tuvi Etzion is a professor of computer science at Technion - Israel Institute of Technology in Haifa, Israel. He has published more than 130 papers in leading scientific journals and IEEE fellow. His research interests include applications of discrete mathematics to problems in computer science and information theory, coding theory, digital sequences in coding and communication, network coding, coding for memories, and combinatorial designs.
