Indexed Swap Matching for Short Patterns

Abstract

Let T be a text of length n and P be a pattern of length m, both strings over a fixed finite alphabet. The Pattern Matching with Swaps problem is to find all occurrences of P in T if adjacent pattern characters can be swapped. 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 provide the first off-line solution for the swap matching problem and the approximate pattern matching problem with swaps. We present a new data-structure called a Swap-transforming Tree. And we give a precise upper-bond of the number of the swapped versions of a pattern. By using the swap-transforming tree, we can solve both problems in time O(λ^mlog ²n) on an O(nH_k) bits indexing data structure. Here λ is a constant. Our solution is more effective when the pattern is short.