We propose a new paradigm for string matching, namely structural matching. In structural matching, the text and pattern contents are not important. Rather, some areas in the text and patterns are singled out, say intervals. A "match" is a text location where a specified relation between the text and pattern areas is satisfied. In particular we define the structural matching problem of Overlap (Parity) Matching. We seek the text locations where all overlaps of the given pattern and text intervals have even length. We show that this problem can be solved in time O(n log m), where the text length is n and the pattern length is m. As an application of overlap matching, we show how to reduce the String Matching with Swaps problem to the overlap matching problem. The String Matching with Swaps problem is the problem of string matching in the presence of local swaps. The best known deterministic upper bound for this problem was O(nm 1/3 log m log #) for a general alphabet #, wher...

Let a text string T of n symbols and a pattern string P of m symbols from alphabet \Sigma be given. A swapped version P 0 of P is a length m string derived from P by a series of local swaps, (i.e. p 0 ` / p `+1 and p 0 `+1 / p ` ) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i of T for which there exists a swapped version P 0 of P with an exact matching of P 0 in location i of T . Recently, some efficient algorithms were developed for this problem. Their time complexity is better than the best known algorithms for pattern matching with mismatches. However, the Approximate Pattern Matching with Swaps problem was not known to be solved faster than the pattern matching with mismatches problem. In the Approximate Pattern Matching with Swaps problem the output is, for every text location i where there is a swapped match of P , the number of swaps necessary to create the swapped vers...

Abstract. In this paper, we revisit the much studied problem of Pattern matching with Swaps (Swap Matching problem, for short). We first present a new graph-theoretic approach to model the problem, which opens a new and so far unexplored avenue to solve the problem. Then, using the model, we devise an efficient algorithm to solve the swap matching problem. The resulting algorithm is an adaptation of the classic shiftor algorithm. For patterns having length similar to the word-size of the target machine, the algorithm runs in O((n + m) log m) time, where n and m are the length of the text and the pattern respectively. 1

We give a randomized algorithm for the Pattern Matching with Swaps problem which runs in O(m log m log j\Sigmaj) time on a text of length 2m \Gamma 1 and a pattern of length m drawn from an alphabet set of size j\Sigmaj. This algorithm gives the correct answer with probability at least 1 \Gamma and does not miss a match. The best deterministic algorithm known for this problem takes O(m polylog(m)) time.

Abstract. The swap matching problem consists if finding a pattern in a text, while allowing for transpositions in the pattern. A new approach using a graph-theoretic model was presented in [6] by Iliopoulos et al. In this paper we present a useful application for this algorithm and provide an analysis of its running time with a naive approach through implementation. 1