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dangibney/Delta_Bounded_Time_Series_Index

Authors: Daniel Gibney, Kaamil Kaka, and Sharma V. Thankachan


Abstract

Cite as

Daniel Gibney, Kaamil Kaka, Sharma V. Thankachan. dangibney/Delta_Bounded_Time_Series_Index (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@misc{dagstuhl-artifact-27610,
   title = {{dangibney/Delta\underlineBounded\underlineTime\underlineSeries\underlineIndex}}, 
   author = {Gibney, Daniel and Kaka, Kaamil and Thankachan, Sharma V.},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:b33cf856db1f9e72d95c00136bf351670d04bfb2;origin=https://github.com/dangibney/Delta_Bounded_Time_Series_Index;visit=swh:1:snp:52d5caa7ab19c280042b595fba258e0dc325c4cd;anchor=swh:1:rev:ace78c25b6ee547d71ac97dc0150dca204559079}{\texttt{swh:1:dir:b33cf856db1f9e72d95c00136bf351670d04bfb2}} (visited on 2026-08-25)},
   url = {https://github.com/dangibney/Delta_Bounded_Time_Series_Index},
   doi = {10.4230/artifacts.27610},
}
Document
Indexing Integer Strings Using Local Difference Bounds

Authors: Daniel Gibney, Kaamil Kaka, and Sharma V. Thankachan

Published in: LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026)


Abstract
Time series data can often be represented as a string T[1..n] over an integer alphabet Σ. A standard approach for indexing such strings is the compressed suffix tree, which supports efficient exact pattern matching using 𝒪(n log |Σ|) bits of space. However, when |Σ| is close to n, as is often the case for time-series data, this yields little to no space savings over the classical Θ(n log n)-bit suffix tree. In this work, we study a different parameter that is often much smaller than |Σ|: the maximum absolute difference between consecutive values in T, denoted by Δ. Although representing T in 𝒪(n log Δ) bits is straightforward, supporting efficient pattern matching within this space bound remains challenging. By leveraging succinct data structure techniques, particularly the FM-index, we obtain a compressed index occupying n log Δ + 𝒪(n) bits. Given a query pattern P[1..m], the index answers counting queries in 𝒪(m log Δ) time and reporting queries in 𝒪(m log Δ + occ ⋅ log n ⋅ log Δ) time, where occ denotes the number of occurrences of P in T. In addition, the structure supports suffix array and inverse suffix array queries in 𝒪(log n ⋅ log Δ) time. Our construction is conceptually simple. We show that the local-difference bound induces a strong form of locality in the Burrows-Wheeler Transform (BWT), allowing the transformed text to be decomposed into regions that each use only a small local alphabet of size 𝒪(Δ). This makes it possible to adapt the classical FM-index so that its space usage depends on Δ rather than the overall alphabet size, while still supporting efficient pattern matching queries.

Cite as

Daniel Gibney, Kaamil Kaka, and Sharma V. Thankachan. Indexing Integer Strings Using Local Difference Bounds. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 151:1-151:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{gibney_et_al:LIPIcs.ESA.2026.151,
  author =	{Gibney, Daniel and Kaka, Kaamil and Thankachan, Sharma V.},
  title =	{{Indexing Integer Strings Using Local Difference Bounds}},
  booktitle =	{34th Annual European Symposium on Algorithms (ESA 2026)},
  pages =	{151:1--151:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-445-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{388},
  editor =	{Bille, Philip and Pettie, Seth and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.151},
  URN =		{urn:nbn:de:0030-drops-272870},
  doi =		{10.4230/LIPIcs.ESA.2026.151},
  annote =	{Keywords: String Algorithms, Pattern Matching, Suffix Trees, Compact Data Structures}
}
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