Document Type

Conference Proceeding

Publication Date

5-27-2026

Department

Department of Computer Science

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 log2 N) 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 logM/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.

Publisher's Statement

© Yakov Nekrich and Saladi Rahul. Publisher’s version of record: 10.4230/LIPIcs.SoCG.2026.81

Publication Title

Leibniz International Proceedings in Informatics Lipics

ISBN

9783959774185

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Version

Publisher's PDF

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