Pattern matching with swaps for short patterns in linear time

The Pattern Matching problem with Swaps consists in finding all occurrences of a pattern P in a text T, when disjoint local swaps in the pattern are allowed. In the Approximate Pattern Matching problem with Swaps one seeks, for every text location with a swapped match of P, the number of swaps necessary to obtain a match at the location. In this paper, we present a new approach for solving both the Swap Matching problem and the Approximate Swap Matching problem in linear time, in the case of short patterns. In particular, we devise a O(nm) general algorithm, named Cross-Sampling, and show an efficient implementation of it, based on bit-parallelism, which achieves O(n) worst-case time and O(s)-space complexity, with patterns whose length is comparable to the word-size of the target machine.