An Efficient Algorithm for Finding All Pairs k-Mismatch Maximal Common Substrings

Identifying long pairwise maximal common substrings among a large set of sequences is a frequently used construct in computational biology, with applications in DNA sequence clustering and assembly. Due to errors made by sequencers, algorithms that can accommodate a small number of differences are of particular interest, but obtaining provably efficient solutions for such problems has been elusive. In this paper, we present a provably efficient algorithm with an expected run time guarantee of O(N log(k) N + occ), where occ is the output size, for the following problem: Given a collection D = {S-1, S-2, ..., S-n} of n sequences of total length N, a length threshold (sic) and a mismatch threshold k >= 0, report all k-mismatch maximal common substrings of length at least (sic) over all pairs of sequences in D. In addition, we present a result showing the hardness of this problem.