Fragmentary Pattern Matching: Complexity, Algorithms and Applications for Analyzing Classic Literary Works

A fragmentary pattern is a multiset of non-empty strings, and it matches a string w if all the strings in it occur within w without any overlaps. We study some fundamental issues on computational complexity related to the matching of fragmentary patterns. We show that the fragmentary pattern matching problem is NP-complete, and the problem to find a fragmentary pattern common to two strings that maximizes the pattern score is NP-hard. Moreover, we propose a polynomialtime approximation algorithm for the fragmentary pattern matching, and show that it achieves a constant worst-case approximation ratio if either the strings in a pattern have the same length, or the importance weights of strings in a pattern are proportional to their lengths.