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arXiv · 2603.22591

Computing and Enumerating Minimal Common Supersequences Between Two Strings

Braeden Sopp·Adiesha Liyanage·Mingyang Gong·Binhai Zhu
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Abstract

Given \(k\) strings each of length at most $n$, computing the shortest common supersequence of them is a well-known NP-hard problem (when \(k\) is unbounded). On the other hand, when \(k=2\), such a shortest common supersequence can be computed in \(O(n^2)\) time using dynamic programming as a textbook example. In this paper, we consider the problem of computing a \emph{minimal} common supersequence and enumerating all minimal common supersequences for \(k=2\) input strings. Our results are summarized as follows. A minimal common supersequence of \(k=2\) input strings can be computed in $O(n)$ time. (The method also works when \(k\) is a constant). All minimal common supersequences between two input strings can be enumerated with a data structure of $O(n^2)$ space and an $O(n)$ time delay, and the data structure can be constructed in $O(n^3)$ time.

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Braeden Sopp, Adiesha Liyanage, Mingyang Gong, Binhai Zhu. 2026-03-23. Computing and Enumerating Minimal Common Supersequences Between Two Strings. https://arxiv.org/abs/2603.22591

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