Matching Patterns with Variables

A pattern p (i.e., a string of variables and terminals) matches a word w, if w can be obtained by uniformly replacing the variables of p by terminal words. The respective matching problem, i.e., deciding whether or not a given pattern matches a given word, is generally NP-complete, but can be solved in polynomial-time for classes of patterns with restricted structure. In this paper we overview a series of recent results related to efficient matching for patterns with variables, as well as a series of extensions of this problem.