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 Hyyrö [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.
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Notes
- 1.
The algorithm of Rick, as recommended in [4], was omitted as it was not competitive in our experiments. This was probably due to its high \(O(\sigma m)\) preprocessing cost.
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Hyyrö, H. (2017). Mining Bit-Parallel LCS-length Algorithms. In: Fici, G., Sciortino, M., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2017. Lecture Notes in Computer Science(), vol 10508. Springer, Cham. https://doi.org/10.1007/978-3-319-67428-5_18
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DOI: https://doi.org/10.1007/978-3-319-67428-5_18
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