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Near-Optimal and Efficient Encoding for Two-Dimensional Range Minimum Queries

Authors Paweł Gawrychowski , Adam Górkiewicz , Srinivasa Rao Satti

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LIPIcs.ESA.2026.51.pdf
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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Encoding
  • Range Minimum Queries
  • Compact structure

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Abstract

We consider the 2D RMQ encoding problem: given an m× n array of mn elements over a total order, encode it such that, for any query rectangle, the position of its maximum element can be reported without accessing the original array. For m ≤ n, it is known how to encode the array in 𝒪(mn min{m, log n}) bits with 𝒪(1)-time queries [Brodal et al., Algorithmica 2012], and also how to obtain an asymptotically optimal encoding consisting of 𝒪(mn log m) bits [Brodal et al., ESA 2013]. However, the latter approach does not prove any guarantee on the query time, and it appears to be inherently sequential: it requires scanning the whole encoding to answer a query. We design a different encoding that uses near-optimal space while allowing for efficient queries. More concretely, for every parameter κ ∈ [1, log log n], our encoding uses 𝒪(κ mn(log m + log log n)) bits and answers 2D RMQ queries in 𝒪(log^{1/κ} n) time.

Cite As Get BibTex

Paweł Gawrychowski, Adam Górkiewicz, and Srinivasa Rao Satti. Near-Optimal and Efficient Encoding for Two-Dimensional Range Minimum Queries. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 51:1-51:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.51

Author Details

Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland
Adam Górkiewicz
  • Institute of Computer Science, University of Wrocław, Poland
Srinivasa Rao Satti
  • Department of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway

Funding

Paweł Gawrychowski and Adam Górkiewicz: Partially supported by the Polish National Science Centre grant number 2023/51/B/ST6/01505.

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