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arXiv · 2504.05742

Linear-space LCS enumeration with quadratic-time delay for two strings

Yoshifumi Sakai
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Abstract

Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted by traceback. However, the need for quadratic space to hold this table can be an obstacle when dealing with long strings. A question that naturally arises in this situation would be whether it is possible to exhaustively search for all LCSs one by one in a time-efficient manner using only a space linear in the LCS length, where we treat read-only memory for storing the strings as excluded from the space consumed. As a part of the answer to this question, we propose an $O(L)$-space algorithm that outputs all distinct LCSs of the strings one by one each in $O(n^2)$ time, where the strings are both of length $n$ and $L$ is the LCS length of the strings.

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Yoshifumi Sakai. 2025-04-08. Linear-space LCS enumeration with quadratic-time delay for two strings. https://arxiv.org/abs/2504.05742

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