Space-efficient approximate string matching allowing inversions in fast average time

An inversion is one of the important operations in bio sequence analysis and the sequence alignment problem is well-studied for efficient bio sequence comparisons. We investigate the string matching problem allowing inversions: Given a pattern P and a text T, find all indices of matching substrings of T when non-overlapping inversions are allowed. We design an O(nm) algorithm using O(m) space, where n is the size of T and m is the size of P. The proposed algorithm improves the space complexity of the best-known algorithm, which runs in O(nm) time with O(m ²) space. We, furthermore, improve the algorithm and achieve O(max{n, min{nm,nm 5-t/2 }}) average runtime for an alphabet of size t, which is faster than O(nm) when t ≥ 4.