Abelian pattern matching in strings

Abstract

Abelian pattern matching is a new class of pattern matching problems. In abelian patterns, the order of the characters in the substrings does not matter, e.g. the strings abbc and babc represent the same abelian pattern a+2b+c. Therefore, unlike classical pattern matching, we do not look for an exact (ordered) occurrence of a substring, rather the aim here is to find any permutation of a given combination of characters that represents the given abelian pattern. In this thesis, we study the problem of abelian pattern matching in strings in a systematic manner, and present several algorithms for exact as well as approximate abelian pattern matching. We also present different strategies for indexing the input text to make the abelian pattern matching more efficient.