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Dynamic Range Minimum Queries on the Ultra-wide Word RAM

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SOFSEM 2025: Theory and Practice of Computer Science (SOFSEM 2025)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15538))

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Abstract

We consider the dynamic range minimum problem on the ultra-wide word RAM model of computation. This model extends the classic w-bit word RAM model with special ultrawords of length \(w^2\) bits that support standard arithmetic and boolean operation and scattered memory access operations that can access w (non-contiguous) locations in memory. The ultra-wide word RAM model captures (and idealizes) modern vector processor architectures.

Our main result is a linear space data structure that supports range minimum queries and updates in \(O(\log \log \log n)\) time. This exponentially improves the time of existing techniques. Our result is based on a simple reduction to prefix minimum computations on sequences \(O(\log n)\) words combined with a new parallel, recursive implementation of these.

Partially supported by the Danish Research Council via grant DFF-8021-002498.

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Authors and Affiliations

  1. Technical University of Denmark, DTU Compute, Kgs. Lyngby, Denmark

    Philip Bille, Inge Li Gørtz, Máximo Pérez López & Tord Stordalen

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  1. Philip Bille
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  2. Inge Li Gørtz
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  3. Máximo Pérez López
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  4. Tord Stordalen
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Correspondence to Philip Bille .

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Editors and Affiliations

  1. Comenius University in Bratislava, Bratislava, Slovakia

    Rastislav Královič

  2. Czech Academy of Sciences, Prague, Czech Republic

    Věra Kůrková

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Bille, P., Gørtz, I.L., Pérez López, M., Stordalen, T. (2025). Dynamic Range Minimum Queries on the Ultra-wide Word RAM. In: Královič, R., Kůrková, V. (eds) SOFSEM 2025: Theory and Practice of Computer Science. SOFSEM 2025. Lecture Notes in Computer Science, vol 15538. Springer, Cham. https://doi.org/10.1007/978-3-031-82670-2_10

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  • DOI: https://doi.org/10.1007/978-3-031-82670-2_10

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