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Encodings for Range Minimum Queries over Bounded Alphabets

Authors Seungbum Jo , Srinivasa Rao Satti

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LIPIcs.CPM.2025.25.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Range minimum queries
  • Encoding data structures
  • Cartesian trees

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Abstract

Range minimum queries (RMQs) are fundamental operations with widespread applications in database management, text indexing and computational biology. While many space-efficient data structures have been designed for RMQs on arrays with arbitrary elements, there has not been any results developed for the case when the alphabet size is small, which is the case in many practical scenarios where RMQ structures are used. In this paper, we investigate the encoding complexity of RMQs on arrays over bounded alphabet. We consider both one-dimensional (1D) and two-dimensional (2D) arrays. For the 1D case, we present a near-optimal space encoding. For constant-sized alphabets, this also supports the queries in constant time. For the 2D case, we systematically analyze the 1-sided, 2-sided, 3-sided and 4-sided queries and derive lower bounds for encoding space, and also matching upper bounds that support efficient queries in most cases. Our results demonstrate that, even with the bounded alphabet restriction, the space requirements remain close to those for the general alphabet case.

Cite As Get BibTex

Seungbum Jo and Srinivasa Rao Satti. Encodings for Range Minimum Queries over Bounded Alphabets. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 25:1-25:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.25

Author Details

Seungbum Jo
  • Chungnam National University, Daejeon, South Korea
Srinivasa Rao Satti
  • Norwegian University of Science and Technology, Trondheim, Norway

Funding

  • Jo, Seungbum: This work was supported by research fund of Chungnam National University.

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