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Optimal-Cost Construction of Shallow Cuttings for 3-D Dominance Ranges in the I/O-Model

Authors Yakov Nekrich , Saladi Rahul

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LIPIcs.SoCG.2026.81.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures and algorithms for data management
  • Theory of computation → Computational geometry
Keywords
  • Data Structures
  • I/O-efficient algorithms
  • Orthogonal Range Searching

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Abstract

Shallow cuttings are a fundamental tool in computational geometry and spatial databases for solving offline and online range searching problems. For a set P of N points in 3-D, at SODA'14, Afshani and Tsakalidis designed an optimal O(N log₂N) time algorithm that constructs shallow cuttings for 3-D dominance ranges in internal memory. Even though shallow cuttings are used in the I/O-model to design space and query efficient range searching data structures, an efficient construction of them is not known till now. In this paper, we design an optimal-cost algorithm to construct shallow cuttings for 3-D dominance ranges. The number of I/Os performed by the algorithm is O (N/B log_{M/B}(N/B)), where B is the block size and M is the memory size. 
As two applications of the optimal-cost construction algorithm, we design fast algorithms for offline 3-D dominance reporting and offline 3-D approximate dominance counting. We believe that our algorithm will find further applications in offline 3-D range searching problems and in improving construction cost of data structures for 3-D range searching problems.

Cite As Get BibTex

Yakov Nekrich and Saladi Rahul. Optimal-Cost Construction of Shallow Cuttings for 3-D Dominance Ranges in the I/O-Model. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.81

Author Details

Yakov Nekrich
  • Michigan Technological University, Houghton, MI, USA
Saladi Rahul
  • Indian Institute of Science, Bangalore, India

Funding

  • Nekrich, Yakov: Supported by the National Science Foundation under NSF grant 2203278.
  • Rahul, Saladi: Supported by the Walmart Center for Tech Excellence at IISc (CSR Grant WMGT-230001) and Anusandhan National Research Foundation (SP/ANRF-24-0043 CRG/2023/005776).

Acknowledgements

The authors thank the reviewers whose detailed feedback helped in improving the presentation of the paper.

References

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