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Approximate Circular Pattern Matching Under Edit Distance

Authors Panagiotis Charalampopoulos , Solon P. Pissis , Jakub Radoszewski , Wojciech Rytter , Tomasz Waleń , Wiktor Zuba

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  • Theory of computation → Pattern matching
Keywords
  • circular pattern matching
  • approximate pattern matching
  • edit distance

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Abstract

In the k-Edit Circular Pattern Matching (k-Edit CPM) problem, we are given a length-n text T, a length-m pattern P, and a positive integer threshold k, and we are to report all starting positions of the substrings of T that are at edit distance at most k from some cyclic rotation of P. In the decision version of the problem, we are to check if any such substring exists. Very recently, Charalampopoulos et al. [ESA 2022] presented 𝒪(nk²)-time and 𝒪(nk log³ k)-time solutions for the reporting and decision versions of k-Edit CPM, respectively. Here, we show that the reporting and decision versions of k-Edit CPM can be solved in 𝒪(n+(n/m) k⁶) time and 𝒪(n+(n/m) k⁵ log³ k) time, respectively, thus obtaining the first algorithms with a complexity of the type 𝒪(n+(n/m) poly(k)) for this problem. Notably, our algorithms run in 𝒪(n) time when m = Ω(k⁶) and are superior to the previous respective solutions when m = ω(k⁴). We provide a meta-algorithm that yields efficient algorithms in several other interesting settings, such as when the strings are given in a compressed form (as straight-line programs), when the strings are dynamic, or when we have a quantum computer.
We obtain our solutions by exploiting the structure of approximate circular occurrences of P in T, when T is relatively short w.r.t. P. Roughly speaking, either the starting positions of approximate occurrences of rotations of P form 𝒪(k⁴) intervals that can be computed efficiently, or some rotation of P is almost periodic (is at a small edit distance from a string with small period). Dealing with the almost periodic case is the most technically demanding part of this work; we tackle it using properties of locked fragments (originating from [Cole and Hariharan, SICOMP 2002]).

Cite As Get BibTex

Panagiotis Charalampopoulos, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń, and Wiktor Zuba. Approximate Circular Pattern Matching Under Edit Distance. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.STACS.2024.24

Author Details

Panagiotis Charalampopoulos
  • Birkbeck, University of London, UK
Solon P. Pissis
  • CWI, Amsterdam, The Netherlands
  • Vrije Universiteit, Amsterdam, The Netherlands
Jakub Radoszewski
  • University of Warsaw, Poland
Wojciech Rytter
  • University of Warsaw, Poland
Tomasz Waleń
  • University of Warsaw, Poland
Wiktor Zuba
  • CWI, Amsterdam, The Netherlands

Funding

  • Pissis, Solon P.: Supported by the PANGAIA and ALPACA projects that have received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreements No 872539 and 956229, respectively.
  • Radoszewski, Jakub: Supported by the Polish National Science Center, grant no. 2022/46/E/ST6/00463.
  • Zuba, Wiktor: Received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement Grant Agreement No 101034253.

Acknowledgements

We thank Tomasz Kociumaka for helpful discussions.

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