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Faster Sliding Window String Indexing in Streams

Authors Philip Bille , Paweł Gawrychowski , Inge Li Gørtz , Simon R. Tarnow

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Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • data structures
  • pattern matching
  • string indexing

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Abstract

The classical string indexing problem asks to preprocess the input string S for efficient pattern matching queries. Bille, Fischer, Gørtz, Pedersen, and Stordalen [CPM 2023] generalized this to the {streaming sliding window string indexing} problem, where the input string S arrives as a stream, and we are asked to maintain an index of the last w characters, called the window. Further, at any point in time, a pattern P might appear, again given as a stream, and all occurrences of P in the current window must be output. We require that the time to process each character of the text or the pattern is worst-case. It appears that standard string indexing structures, such as suffix trees, do not provide an efficient solution in such a setting, as to obtain a good worst-case bound, they necessarily need to work right-to-left, and we cannot reverse the pattern while keeping a worst-case guarantee on the time to process each of its characters. Nevertheless, it is possible to obtain a bound of 𝒪(log w) (with high probability) by maintaining a hierarchical structure of multiple suffix trees. 
We significantly improve this upper bound by designing a black-box reduction to maintain a suffix tree under prepending characters to the current text. By plugging in the known results, this allows us to obtain a bound of 𝒪(log log w +log log σ) (with high probability), where σ is the size of the alphabet. Further, we introduce an even more general problem, called the {streaming dynamic window string indexing}, where the goal is to maintain the current text under adding and deleting characters at either end and design a similar black-box reduction.

Cite As Get BibTex

Philip Bille, Paweł Gawrychowski, Inge Li Gørtz, and Simon R. Tarnow. Faster Sliding Window String Indexing in Streams. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CPM.2024.8

Author Details

Philip Bille
  • Technical University of Denmark, Lyngby, Denmark
Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Inge Li Gørtz
  • Technical University of Denmark, Lyngby, Denmark
Simon R. Tarnow
  • Technical University of Denmark, Lyngby, Denmark

Funding

  • Bille, Philip: Supported by the Independent Research Fund Denmark (DFF-9131-00069B and 10.46540/3105-00302B).
  • Gørtz, Inge Li: Supported by the Independent Research Fund Denmark (DFF-9131-00069B and 10.46540/3105-00302B).

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