A Parallel Algorithm for Fixed-Length Approximate String-Matching with k-mismatches

Abstract

This paper deals with the approximate string-matching problem with Hamming distance. The approximate string-matching with kmismatches problem is to find all locations at which a query of length m matches a factor of a text of length n with k or fewer mismatches. The approximate string-matching algorithms have both pleasing theoretical features, as well as direct applications, especially in computational biology. We consider a generalisation of this problem, the fixed-length approximate string-matching with k-mismatches problem: given a text t, a pattern x and an integer ℓ, search for all the occurrences in t of all factors of x of length ℓ with k or fewer mismatches with a factor of t. We present a practical parallel algorithm of comparable simplicity that requires only O(nm⌈ℓ/w⌉ p) time, where w is the word size of the machine (e.g. 32 or 64 in practice) and p the number of processors. Thus the algorithm's performance is independent of k and the alphabet size |Σ|. The proposed parallel algorithm makes use of message-passing parallelism model, and word-level parallelism for efficient approximate string-matching.

libFLASM: a software library for fixed-length approximate string matching

“…We adapted it to search for all factors of x of length ℓ in t in order to solve the FLASM problem. For the Hamming distance function, we used our own implementation [40] of the MaxShiftM algorithm [7], which solves the FLASM problem under the Hamming distance model. Notice that both functions provided by the library work for an arbitrary length ℓ using multiple computer words, thus delivering the -time and -space complexity of the proposed algorithms.…”

“…The FLASM problem can be solved efficiently under the edit [6] or the Hamming [7] distance model; both algorithms make extensive use of bit-vector techniques to compute the solution. These techniques take advantage of low-level processor operations on computer words.…”

“…For the Hamming distance model, we use our own implementation (a preliminary version appeared in [40]) of the MaxShiftM algorithm [7], and for the edit distance model we generalise the SeqAn [41] implementation of Myers’ bit-vector algorithm [6] for approximate string matching. Both of these implementations are based on dynamic-programming approaches accelerated by the use of bit-vector techniques to achieve their goals.…”

MoTeX-II: structured MoTif eXtraction from large-scale datasets

“…Crochemore, Iliopoulos, and Pissis devised an analogous algorithm [22] that solves the analogous problem under the Hamming distance model with the same time and space complexity.…”

“…Let M [0.. n ,0.. m ] be a DP matrix, where M[ i , j ] contains the Hamming distance between factor y [max{1, i − k +1}.. i ] of y and factor x [max{1, j − k +1}.. j ] of x , for all 1≤ i ≤ n , 1≤ j ≤ m . Crochemore, Iliopoulos, and Pissis devised an analogous algorithm [ 22 ] that solves the analogous problem under the Hamming distance model with the same time and space complexity.…”