Mining Bit-Parallel LCS-length Algorithms

Abstract

Some of the most efficient algorithms for computing the length of a longest common subsequence (LLCS) between two strings are based on so-called “bit-parallelism”. They achieve \(O(\lceil m/w \rceil n)\) time, where m and n are the string lengths and w is the computer word size. The first such algorithm was presented by Allison and Dix [3] and performs 6 bit-vector operations per step. The number of operations per step has later been improved to 5 by Crochemore et al. [5] and to 4 by Hyyro [6]. In this short paper we explore whether further improvement is possible. We find that under fairly reasonable assumptions, the LLCS problem requires at least 4 bit-vector operations per step. As a byproduct we also present five new 4-operation bit-parallel LLCS algorithms.