2 research outputs found
A Parameterized Study of Maximum Generalized Pattern Matching Problems
The generalized function matching (GFM) problem has been intensively studied
starting with [Ehrenfeucht and Rozenberg, 1979]. Given a pattern p and a text
t, the goal is to find a mapping from the letters of p to non-empty substrings
of t, such that applying the mapping to p results in t. Very recently, the
problem has been investigated within the framework of parameterized complexity
[Fernau, Schmid, and Villanger, 2013].
In this paper we study the parameterized complexity of the optimization
variant of GFM (called Max-GFM), which has been introduced in [Amir and Nor,
2007]. Here, one is allowed to replace some of the pattern letters with some
special symbols "?", termed wildcards or don't cares, which can be mapped to an
arbitrary substring of the text. The goal is to minimize the number of
wildcards used.
We give a complete classification of the parameterized complexity of Max-GFM
and its variants under a wide range of parameterizations, such as, the number
of occurrences of a letter in the text, the size of the text alphabet, the
number of occurrences of a letter in the pattern, the size of the pattern
alphabet, the maximum length of a string matched to any pattern letter, the
number of wildcards and the maximum size of a string that a wildcard can be
mapped to.Comment: to appear in Proc. IPEC'1