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

Abstract

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 $O(N\log ^k N+\mathsf {occ})$, where $\mathsf {occ}$ is the output size, for the following problem: Given a collection ${\mathcal D}=\{S_1,S_2,\dots , S_n\}$ of n sequences of total length N, a length threshold $\phi$ and a mismatch threshold $k \ge 0$, report all k-mismatch maximal common substrings of length at least $\phi$ over all pairs of sequences in ${\mathcal D}$. In addition, we present a result showing the hardness of this problem.