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Internal Shortest Absent Word Queries

Authors Golnaz Badkobeh , Panagiotis Charalampopoulos , Solon P. Pissis

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  • Theory of computation → Pattern matching
Keywords
  • string algorithms
  • internal queries
  • shortest absent word
  • bit parallelism

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Abstract

Given a string T of length n over an alphabet Σ ⊂ {1,2,…,n^{𝒪(1)}} of size σ, we are to preprocess T so that given a range [i,j], we can return a representation of a shortest string over Σ that is absent in the fragment T[i]⋯ T[j] of T. For any positive integer k ∈ [1,log log_σ n], we present an 𝒪((n/k)⋅ log log_σ n)-size data structure, which can be constructed in 𝒪(nlog_σ n) time, and answers queries in time 𝒪(log log_σ k).

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Golnaz Badkobeh, Panagiotis Charalampopoulos, and Solon P. Pissis. Internal Shortest Absent Word Queries. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CPM.2021.6

Author Details

Golnaz Badkobeh
  • Department of Computing, Goldsmiths University of London, UK
Panagiotis Charalampopoulos
  • Efi Arazi School of Computer Science, The Interdisciplinary Center Herzliya, Israel
Solon P. Pissis
  • CWI, Amsterdam, The Netherlands
  • Vrije Universiteit, Amsterdam, The Netherlands

Funding

  • Charalampopoulos, Panagiotis: Supported by the Israel Science Foundation grant 592/17.

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