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DOI: 10.4230/LIPIcs.STACS.2026.62

Relative Compressed Reverse Suffix Array

Authors: Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract

Suffix trees and suffix arrays are two fundamental data structures in the field of string algorithms. For a string (a.k.a. text or sequence) of length n over an alphabet of size σ, these structures typically require O(nlog n) bits of space. The FM-index provides a compressed representation of the suffix array in ≈ nlog σ bits, allowing for efficient queries on both the suffix array and its inverse array in near logarithmic time. In certain applications, such as approximate pattern matching (i.e., with wildcards, mismatches, edits), there is a need to access the suffix array of a text, as well as the suffix array of text’s reverse. Motivated by this, we explore the possibility of encoding the suffix array of the reversed text in a compact form, assuming the availability of the FM-index for the original text. Our first solution is an O(n)-bit (relative) encoding of the suffix array of the reversed text, with the time for decoding an entry being only O(log^*n) times that of decoding an entry in the text’s suffix array using FM-index. We then demonstrate how to reduce the space to O(n/κ) bits for a parameter κ, while multiplicative factor in time becomes approximately O(κlog^*n+κ³). We can also support inverse suffix array and longest common extension queries on the reversed text. These results are achieved through some careful and non-trivial application of various succinct data structure techniques.

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Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan. Relative Compressed Reverse Suffix Array. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kulekci_et_al:LIPIcs.STACS.2026.62,
  author =	{Kulekci, Muhammed Oguzhan and Parthasarathi, Mano Prakash and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Relative Compressed Reverse Suffix Array}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{62:1--62:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.62},
  URN =		{urn:nbn:de:0030-drops-255512},
  doi =		{10.4230/LIPIcs.STACS.2026.62},
  annote =	{Keywords: String Matching, Text Indexing, Data Structures, Suffix Trees}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.88

Repetition Aware Text Indexing for Matching Patterns with Wildcards

Authors: Daniel Gibney, Jackson Huffstutler, Mano Prakash Parthasarathi, and Sharma V. Thankachan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

We study the problem of indexing a text T[1..n] to support pattern matching with wildcards. The input of a query is a pattern P[1..m] containing h ∈ [0, k] wildcard (a.k.a. don't care) characters and the output is the set of occurrences of P in T (i.e., starting positions of substrings of T that matches P), where k = o(log n) is fixed at index construction. A classic solution by Cole et al. [STOC 2004] provides an index with space complexity O(n ⋅ (clog n)^k/k!)) and query time O(m+2^h log log n+occ), where c > 1 is a constant, and occ denotes the number of occurrences of P in T. We introduce a new data structure that significantly reduces space usage for highly repetitive texts while maintaining efficient query processing. Its space (in words) and query time are as follows: O(δ log (n/δ)⋅ c^k (1+(log^k (δ log n))/k!)) and O((m+2^h +occ)log n)) The parameter δ, known as substring complexity, is a recently introduced measure of repetitiveness that serves as a unifying and lower-bounding metric for several popular measures, including the number of phrases in the LZ77 factorization (denoted by z) and the number of runs in the Burrows-Wheeler Transform (denoted by r). Moreover, O(δ log (n/δ)) represents the optimal space required to encode the data in terms of n and δ, helping us see how close our space is to the minimum required. In another trade-off, we match the query time of Cole et al.’s index using O(n+δ log (n/δ) ⋅ (clogδ)^{k+ε}/k!) space, where ε > 0 is an arbitrarily small constant. We also demonstrate how these techniques can be applied to a more general indexing problem, where the query pattern includes k-gaps (a gap can be interpreted as a contiguous sequence of wildcard characters).

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Daniel Gibney, Jackson Huffstutler, Mano Prakash Parthasarathi, and Sharma V. Thankachan. Repetition Aware Text Indexing for Matching Patterns with Wildcards. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 88:1-88:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gibney_et_al:LIPIcs.ICALP.2025.88,
  author =	{Gibney, Daniel and Huffstutler, Jackson and Parthasarathi, Mano Prakash and Thankachan, Sharma V.},
  title =	{{Repetition Aware Text Indexing for Matching Patterns with Wildcards}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{88:1--88:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.88},
  URN =		{urn:nbn:de:0030-drops-234656},
  doi =		{10.4230/LIPIcs.ICALP.2025.88},
  annote =	{Keywords: Pattern Matching, Text Indexing, Wildcard Matching}
}

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Documents authored by Parthasarathi, Mano Prakash

Relative Compressed Reverse Suffix Array

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Repetition Aware Text Indexing for Matching Patterns with Wildcards

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