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Sorted Consecutive Occurrence Queries in Substrings

Authors Waseem Akram , Takuya Mieno

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • string algorithm
  • consecutive occurrences
  • suffix tree

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Abstract

The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for preprocessing and a pattern P of length m as a query, the goal is to report all occurrences of P as substrings of T. Navarro and Thankachan [CPM 2015, Theor. Comput. Sci. 2016] introduced a variant of this problem called the gap-bounded consecutive occurrence query, which reports pairs of consecutive occurrences of P in T such that their gaps (i.e., the distances between them) lie within a query-specified range [g₁, g₂]. Recently, Bille et al. [FSTTCS 2020, Theor. Comput. Sci. 2022] proposed the top-k close consecutive occurrence query, which reports the k closest consecutive occurrences of P in T, sorted in non-decreasing order of distance. Both problems are optimally solved in query time with O(n log n)-space data structures.
In this paper, we generalize these problems to the range query model, which focuses only on occurrences of P in a specified substring T[a.. b] of T. Our contributions are as follows:  
- We propose an O(n log² n)-space data structure that answers the range top-k consecutive occurrence query in O(|P| + log log n + k) time. 
- We propose an O(n log^{2+ε} n)-space data structure that answers the range gap-bounded consecutive occurrence query in O(|P| + log log n + output) time, where ε is a positive constant and output denotes the number of outputs.  Additionally, as by-products, we present algorithms for geometric problems involving weighted horizontal segments in a 2D plane, which are of independent interest.

Cite As Get BibTex

Waseem Akram and Takuya Mieno. Sorted Consecutive Occurrence Queries in Substrings. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.24

Author Details

Waseem Akram
  • Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, India
Takuya Mieno
  • Department of Computer and Network Engineering, University of Electro-Communications, Chofu, Japan

Funding

  • Mieno, Takuya: JSPS KAKENHI Grant Number JP24K20734.

Acknowledgements

We sincerely thank the anonymous referees for their thorough review and valuable feedback, which have contributed to enhancing the clarity and quality of this paper. The first author extends his heartfelt gratitude to his thesis supervisor, Prof. Sanjeev Saxena, for his invaluable guidance and unwavering support throughout this work.

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