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Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching

Authors Kento Iseri, Tomohiro I , Diptarama Hendrian , Dominik Köppl , Ryo Yoshinaka , Ayumi Shinohara

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Author Details

Kento Iseri
  • Kyushu Institute of Technology, Japan
Tomohiro I
  • Kyushu Institute of Technology, Japan
Diptarama Hendrian
  • Tokyo Medical and Dental University, Japan
Dominik Köppl
  • University of Yamanashi, Japan
Ryo Yoshinaka
  • Tohoku University, Sendai, Japan
Ayumi Shinohara
  • Tohoku University, Sendai, Japan

Funding

  • I, Tomohiro: KAKENHI (Grant Numbers 19K20213, 22K11907).
  • Köppl, Dominik: KAKENHI (Grant Number 23H04378).
  • Yoshinaka, Ryo: KAKENHI (Grant Numbers 18K11150, 20H05703, 23K11325, 24K14827).
  • Shinohara, Ayumi: KAKENHI (Grant Number 21K11745).

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Kento Iseri, Tomohiro I, Diptarama Hendrian, Dominik Köppl, Ryo Yoshinaka, and Ayumi Shinohara. Breaking a Barrier in Constructing Compact Indexes for Parameterized Pattern Matching. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 89:1-89:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.89

Abstract

A parameterized string (p-string) is a string over an alphabet (Σ_s ∪ Σ_p), where Σ_s and Σ_p are disjoint alphabets for static symbols (s-symbols) and for parameter symbols (p-symbols), respectively. Two p-strings x and y are said to parameterized match (p-match) if and only if x can be transformed into y by applying a bijection on Σ_p to every occurrence of p-symbols in x. The indexing problem for p-matching is to preprocess a p-string T of length n so that we can efficiently find the occurrences of substrings of T that p-match with a given pattern. Let σ_s and respectively σ_p be the numbers of distinct s-symbols and p-symbols that appear in T and σ = σ_s + σ_p. Extending the Burrows-Wheeler Transform (BWT) based index for exact string pattern matching, Ganguly et al. [SODA 2017] proposed parameterized BWTs (pBWTs) to design the first compact index for p-matching, and posed an open problem on how to construct the pBWT-based index in compact space, i.e., in O(n lg |Σ_s ∪ Σ_p|) bits of space. Hashimoto et al. [SPIRE 2022] showed how to construct the pBWT for T, under the assumption that Σ_s ∪ Σ_p = [0..O(σ)], in O(n lg σ) bits of space and O(n (σ_p lg n)/(lg lg n)) time in an online manner while reading the symbols of T from right to left. In this paper, we refine Hashimoto et al.’s algorithm to work in O(n lg σ) bits of space and O(n (lg σ_p lg n)/(lg lg n)) time in a more general assumption that Σ_s ∪ Σ_p = [0..n^{O(1)}]. Our result has an immediate application to constructing parameterized suffix arrays in O(n (lg σ_p lg n)/(lg lg n)) time and O(n lg σ) bits of working space. We also show that our data structure can support backward search, a core procedure of BWT-based indexes, at any stage of the online construction, making it the first compact index for p-matching that can be constructed in compact space and even in an online manner.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Index for parameterized pattern matching
  • Parameterized Burrows-Wheeler Transform
  • Online construction

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