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Absent Subsequences in Words
- Source :
- Fundamenta Informaticae, Volume 189, Issues 3-4: Reachability Problems 2020 and 2021 (October 14, 2023) fi:9221
- Publication Year :
- 2021
-
Abstract
- An absent factor of a string $w$ is a string $u$ which does not occur as a contiguous substring (a.k.a. factor) inside $w$. We extend this well-studied notion and define absent subsequences: a string $u$ is an absent subsequence of a string $w$ if $u$ does not occur as subsequence (a.k.a. scattered factor) inside $w$. Of particular interest to us are minimal absent subsequences, i.e., absent subsequences whose every subsequence is not absent, and shortest absent subsequences, i.e., absent subsequences of minimal length. We show a series of combinatorial and algorithmic results regarding these two notions. For instance: we give combinatorial characterisations of the sets of minimal and, respectively, shortest absent subsequences in a word, as well as compact representations of these sets; we show how we can test efficiently if a string is a shortest or minimal absent subsequence in a word, and we give efficient algorithms computing the lexicographically smallest absent subsequence of each kind; also, we show how a data structure for answering shortest absent subsequence-queries for the factors of a given string can be efficiently computed.<br />Comment: An extended abstract appeared in the proceedings of the 15th International Conference on Reachability Problems RP2021
Details
- Database :
- arXiv
- Journal :
- Fundamenta Informaticae, Volume 189, Issues 3-4: Reachability Problems 2020 and 2021 (October 14, 2023) fi:9221
- Publication Type :
- Report
- Accession number :
- edsarx.2108.13968
- Document Type :
- Working Paper