A systolic architecture with linear space complexity for longest common subsequence problem

Abstract

The longest common subsequence (LCS) problem is to find an LCS of two strings and the length of the LCS (LLCS). Many previous works focused on reducing the processing time. However, most require too large memory space in total, resulting in being not suitable for hardware implementation. In this paper, we propose a hardware-implementable algorithm and its systolic architecture. The algorithm achieves linear space complexity, and the systolic architecture is feasible for hardware implementation. For two given strings with their lengths of m and n, the algorithm consumes less time complexity when the LLCS is approaching to the minimum of m and n. Furthermore, a scalable architecture is proposed to deal with the LCS problems of two huge strings, whose lengths are far more than m and n. Therefore, our scalable systolic architecture with linear space complexity for the LCS problem is suitable for hardware implementation, and the synthesized results show that our architecture is more efficient.