Row-wise Tiling for the Myers’ Bit-Parallel Approximate String Matching Algorithm

Abstract

Given a text T[1..n] and a pattern P[1..m] the classic dynamic programming algorithm for computing the edit distance between P and every location of T runs in time O(nm). The bit-parallel computation of the dynamic programming matrix [6] runs in time $O(n \left\lceil m/w \right\rceil)$, where w is the number of bits in computer word. We present a new method that rearranges the bit-parallel computations, achieving time $O(\left\lceil n/w \right\rceil (m+\sigma\log_2(\sigma))+n)$, where σ is the size of the alphabet. The algorithm is then modified to solve the k differences problem. The expected running time is $O(\left\lceil n/w \right\rceil (L(k)+\sigma\log_2(\sigma))+R)$, where L(k) depends on k, and R is the number of occurrences. The space usage is O(σ + m). It is in practice much faster than the existing $O(n \left\lceil k/w \right\rceil)$ algorithm [6]. The new method is applicable only for small (e.g. dna) alphabets, but this becomes the fastest algorithm for small m, or moderate k/m. If we want to search multiple patterns in a row, the method becomes attractive for large alphabet sizes too. We also consider applying 128-bit vector instructions for bit-parallel computations.