Sequences and the de Bruijn Graph: Properties, Constructions, and Applications

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.