Alignment Space

Abstract

This chapter discusses the theory of the distance induced by the sequence alignment, which is called alignment distance. We refer to the space caused by alignment as the alignment space. This problem has been discussed in many other fields, such as computer science, information and coding theory, cryptography, DNA computing, etc. Many similar distances have been defined, such as the Levenshtein distance, evolution distance etc. The alignment space is a typical non-linear space. The first problem is whether or not it forms a metric. After the definition of alignment, we give a precise proof of the existence of metric space. We use the modulus structure as the data structure for alignment. In addition to the discussion concerning the relationship between maximum score alignment and minimum penalty alignment, we also discuss the relationship between the alignment distance and Levenshtein distance. To further understand the alignment space structure, the counting theorem and alignment spheroid are presented. Finally, we introduce operations performed on the alignment space.