Absent Subsequences in Words

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING Fundamenta Informaticae Pub Date : 2023-10-26 DOI:10.3233/fi-222159
Maria Kosche, Tore Koß, Florin Manea, Stefan Siemer
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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.
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单词中的缺席子序列
字符串w的缺席因子是一个字符串u,它不作为w内的连续子串(也称为因子)出现。我们扩展了这个研究得很好的概念并定义了缺席子序列:字符串u是字符串w的一个缺席子序列,如果u不是作为w中的子序列(也称为分散因子)出现。我们特别感兴趣的是最小缺席子序列,即每个子序列都不缺席的缺席子序列,以及最短缺席子序列,即最小长度的缺席子序列。我们展示了一系列关于这两个概念的组合和算法结果。例如:我们给出了一个词中最小和最短的缺席子序列集合的组合特征,以及这些集合的紧表示;我们展示了如何有效地测试字符串是否为单词中最短或最小的缺席子序列,并给出了计算每种类型的字典最小缺席子序列的有效算法;此外,我们还展示了如何有效地计算用于回答给定字符串因子的最短缺席子序列查询的数据结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Fundamenta Informaticae
Fundamenta Informaticae 工程技术-计算机:软件工程
CiteScore
2.00
自引率
0.00%
发文量
61
审稿时长
9.8 months
期刊介绍: Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.
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