The Edit Distance to k-Subsequence Universality

Day, Joel D.; Fleischmann, Pamela; Kosche, Maria; Koß, Tore; Manea, Florín; Siemer, Stefan

doi:10.4230/lipics.stacs.2021.25

Cited by 7 publications

(12 citation statements)

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“…For instance, it can be used to directly compare two words w. r. t. their universality index, or serve as a starting point for the analysis of the set of missing subsequences of words. See, for instance, [7,17,22,21,18,39].…”

Section: Universalitymentioning

confidence: 99%

“…In this work we overview a series of algorithmic, combinatorial, and complexity theoretic results concerning subsequences. For their original presentation, please see [7,17,20,29,38,39,18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…For the case of classical subsequences, the accent of our presentation is put on analysis problems (as matching is trivial). We survey results related to the equivalence and universality problems originally presented in [7,17,20,29,38].…”

Section: Introductionmentioning

confidence: 99%

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Combinatorial Algorithms for Subsequence Matching: A Survey

Kosche

Koß

Manea

et al. 2022

Electron. Proc. Theor. Comput. Sci.

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Section: Universalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combinatorial Algorithms for Subsequence Matching: A Survey

Kosche

Koß

Manea

et al. 2022

Electron. Proc. Theor. Comput. Sci.

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“…This is a common assumption in string algorithms: the input alphabet is said to be an integer alphabet, see also the discussion in, e.g., [16]. For its use in the particular case of algorithms related to subsequences see, for instance, [29,21].…”

Section: Algorithmsmentioning

confidence: 99%

“…Two concepts seemed to play an important role in all these investigations: on the one hand, the notion of distinguishing word, i.e., the shortest subsequence present in one string and absent from the other. On the other hand, the notion of universality index of a string [4,21], i.e., the largest k such that the string contains as subsequences all possible strings of length at most k; that is, the length of the shortest subsequence absent from that string, minus 1.…”

Section: Introductionmentioning

confidence: 99%

Absent Subsequences in Words

Kosche¹,

Koß²,

Manea³

et al. 2021

Preprint

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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 subsequencequeries for the factors of a given string can be efficiently computed.

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