Fast algorithms for window accumulated subsequence matching problem

Abstract

A subsequence of a string T is any string that can be obtained by removing zero or more symbols from T. The paper deals with the Window Accumulated Subsequence matching Problem (WASP), which is defined as follows: Given two strings, the text T and the pattern P, and a positive integer w, the window size, find the number of size w substrings of T that contain P as a subsequence. Three algorithms for this problem are introduced: a bit-parallel approach, an algorithm preprocessing the pattern, and an algorithm preprocessing the text. The bit-parallel approach outperforms the state-of-the-art algorithm, and the other two algorithms outperform the bit-parallel approach for small alphabets, short patterns, and windows that are not much larger than the pattern. Furthermore, a preprocessing of the text that solves WASP for a fixed window size and each possible pattern of a given size is described. This is beneficial when we are to solve WASP for a single text and multiple patterns, because when the text is preprocessed, a solution is provided promptly.