Parameterized Searching with Mismatches for Run-Length Encoded Strings

Abstract

Two strings y and y′ of equal length over respective alphabets Σ _y and Σ _y′ are said to parameterized match if there exists a bijection π: Σ _y →Σ _y′ such that π(y ) = y′ , i.e., renaming each character of y according to its corresponding element under π yields y′. (Here we assume that all symbols of both alphabets are used somewhere.) Two natural problems are then parameterized matching, which consists of finding all positions of some text x where a pattern y parameterized matches a substring of x , and approximate parameterized matching, which seeks, at each location of x , a bijection π maximizing the number of parameterized matches at that location.