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Repetition Detection in a Dynamic String

Authors Amihood Amir, Itai Boneh, Panagiotis Charalampopoulos , Eitan Kondratovsky

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Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • string algorithms
  • dynamic algorithms
  • squares
  • repetitions
  • runs

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Abstract

A string UU for a non-empty string U is called a square. Squares have been well-studied both from a combinatorial and an algorithmic perspective. In this paper, we are the first to consider the problem of maintaining a representation of the squares in a dynamic string S of length at most n. We present an algorithm that updates this representation in n^o(1) time. This representation allows us to report a longest square-substring of S in O(1) time and all square-substrings of S in O(output) time. We achieve this by introducing a novel tool - maintaining prefix-suffix matches of two dynamic strings. 
We extend the above result to address the problem of maintaining a representation of all runs (maximal repetitions) of the string. Runs are known to capture the periodic structure of a string, and, as an application, we show that our representation of runs allows us to efficiently answer periodicity queries for substrings of a dynamic string. These queries have proven useful in static pattern matching problems and our techniques have the potential of offering solutions to these problems in a dynamic text setting.

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Amihood Amir, Itai Boneh, Panagiotis Charalampopoulos, and Eitan Kondratovsky. Repetition Detection in a Dynamic String. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ESA.2019.5

Author Details

Amihood Amir
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel
Itai Boneh
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel
Panagiotis Charalampopoulos
  • Department of Informatics, King’s College London, London, UK, Efi Arazi School of Computer Science, The Interdisciplinary Center Herzliya, Herzliya, Israel
Eitan Kondratovsky
  • Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

Funding

  • Amir, Amihood: Supported by Israel Science Foundation (ISF) grant 1475/18 and United States - Israel Binational Science Foundation (BSF) grant 2018141.
  • Charalampopoulos, Panagiotis: Partially supported by Israel Science Foundation (ISF) grant 794/13.

Acknowledgements

We warmly thank Tomasz Kociumaka for useful discussions.

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