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A Textbook Solution for Dynamic Strings

Authors Zsuzsanna Lipták , Francesco Masillo , Gonzalo Navarro

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Author Details

Zsuzsanna Lipták
  • Dipartimento di Informatica, University of Verona, Italy
Francesco Masillo
  • Dipartimento di Informatica, University of Verona, Italy
Gonzalo Navarro
  • Center for Biotechnology and Bioengineering (CeBiB), Department of Computer Science, University of Chile, Chile

Funding

  • Lipták, Zsuzsanna: Partially funded by the MUR PRIN project Nr. 2022YRB97K 'PINC' (Pangenome INformatiCs. From Theory to Applications) and by the INdAM-GNCS Project CUP_E53C23001670001 (Compressione, indicizzazione, analisi e confronto di dati biologici).
  • Navarro, Gonzalo: Funded by Basal Funds FB0001, Mideplan, Chile, and Fondecyt Grant 1-230755, Chile.

Cite AsGet BibTex

Zsuzsanna Lipták, Francesco Masillo, and Gonzalo Navarro. A Textbook Solution for Dynamic Strings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 86:1-86:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.86

Abstract

We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem can be solved in optimal time O(log N) whp for the updates and O(1) worst-case time for the queries, where N is the total collection size [Gawrychowski et al., SODA 2018]. We present here a much simpler solution based on a forest of enhanced splay trees (FeST), where both the updates and the substring comparison take O(log n) amortized time, n being the lengths of the strings involved. The longest common prefix of length 𝓁 is computed in O(log n + log²𝓁) amortized time. Our query results are correct whp. Our simpler solution enables other more general updates in O(log n) amortized time, such as reversing a substring and/or mapping its symbols. We can also regard substrings as circular or as their omega extension.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • dynamic strings
  • splay trees
  • dynamic data structures
  • LCP
  • circular strings

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