Year: 2025
Type: preprint
Abstract: Given a string $w$, another string $v$ is said to be a subsequence of $w$ if $v$ can be obtained from $w$ by removing some of its letters; on the other hand, $v$ is called an absent subsequence of $w$ if $v$ is not a subsequence of $w$. The existing literature on absent subsequences focused on understanding, for a string $w$, the set of its shortest absent subsequences (i.e., the shortest strings which are absent subsequences of $w$) and that of its minimal absent subsequences (i.e., those strings which are absent subsequences of $w$ but whose every proper subsequence occurs in $w$). Our contributions to this area of research are the following. Firstly, we present optimal algorithms (with linear time preprocessing and output-linear delay) for the enumeration of the shortest and, respectively, minimal absent subsequences. Secondly, we present optimal algorithms for the incremental enumeration of these strings with linear time preprocessing and constant delay; in this setting, we only output short edit-scripts showing how the currently enumerated string differs from the previous one. Finally, we provide an efficient algorithm for identifying a longest minimal absent subsequence of a string. All our algorithms improve the state-of-the-art results for the aforementioned problems.
Source: arXiv (Cornell University)
Institution: University of Göttingen
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4417523335