Sequential and parallel algorithms for all-pair [formula omitted]-mismatch maximal common substrings

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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. Formally, let D be a collection of n sequences of total length N, ϕ be a length threshold, and k be a mismatch threshold. The goal is to identify and report all k-mismatch maximal common substrings of length at least ϕ over all pairs of strings in D. Heuristics based on seed-and-extend style filtering techniques are often employed in such applications. However, such methods cannot provide any provably efficient run time guarantees. To this end, we present a sequential algorithm with an expected run time of O(NlogkN+occ), where occ is the output size. We then present a distributed memory parallel algorithm with an expected run time of ONplogN+occlogkN using Ologk+1N expected rounds of global communications, under some realistic assumptions, where p is the number of processors. Finally, we demonstrate the performance and scalability of our algorithms using experiments on large high throughput sequencing data.