A graph approach to the threshold all-against-all substring matching problem

We present a novel graph model and an efficient algorithm for solving the “threshold all against all” problem, which involves searching two strings (with length <i>M</i> and <i>N</i>, respectively) for all maximal approximate substring matches of length at least <i>S</i>, with up to <i>K</i> differences. Our algorithm solves the problem in time <i>O</i>(<i>MNK</i><sub>3</sub>), which is a considerable improvement over the previous known bound for this problem. We also provide experimental evidence that, in practice, our algorithm exhibits a better performance than its worst-case running time.

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