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Relative Compressed Reverse Suffix Array

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

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Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • String Matching
  • Text Indexing
  • Data Structures
  • Suffix Trees

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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) https://doi.org/10.4230/LIPIcs.STACS.2026.62

Author Details

Muhammed Oguzhan Kulekci
  • Miami University, Oxford, OH, USA
Mano Prakash Parthasarathi
  • North Carolina State University, Raleigh, NC, USA
Rahul Shah
  • Louisiana State University, Baton Rouge, LA, USA
Sharma V. Thankachan
  • North Carolina State University, Raleigh, NC, USA

Funding

  • Parthasarathi, Mano Prakash: U.S. National Science Foundation (NSF) award CCF-2315822.
  • Shah, Rahul: U.S. NSF awards CCF-2434261 and CCF-2137057
  • Thankachan, Sharma V.: U.S. NSF awards CCF-2316691 and CCF-2315822.

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