DROPS

Document

DOI: 10.4230/LIPIcs.SoCG.2025.77

Dynamic Maximum Depth of Geometric Objects

Authors: Subhash Suri, Jie Xue, Xiongxin Yang, and Jiumu Zhu

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract

Given a set of geometric objects in the plane (rectangles, squares, disks etc.), its maximum depth (or geometric clique) is the largest number of objects with a common intersection. In this paper, we present data structures for dynamically maintaining the maximum depth under insertions and deletions of geometric objects, with sublinear update time. We achieve the following results: - a 1/k-approximate dynamic maximum-depth data structure for (axis-parallel) rectangles with O(n^{1/(k+1)} log n) amortized update time, for any fixed k ∈ ℤ^+. In particular, when k = 1, this gives an exact data structure for rectangles with O(√n log n) amortized update time, almost matching the best known bound for the offline version of the problem. - a (1/2-ε)-approximate dynamic maximum-depth data structure for disks with n^{2/3} log^{O(1)}n amortized update time, for any constant ε > 0. Having exact data structures for disks with sublinear update time is unlikely, since the static maximum-depth problem for disks is 3SUM-hard and thus does not admit subquadratic-time algorithms.

Cite as

Subhash Suri, Jie Xue, Xiongxin Yang, and Jiumu Zhu. Dynamic Maximum Depth of Geometric Objects. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 77:1-77:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{suri_et_al:LIPIcs.SoCG.2025.77,
  author =	{Suri, Subhash and Xue, Jie and Yang, Xiongxin and Zhu, Jiumu},
  title =	{{Dynamic Maximum Depth of Geometric Objects}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{77:1--77:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.77},
  URN =		{urn:nbn:de:0030-drops-232295},
  doi =		{10.4230/LIPIcs.SoCG.2025.77},
  annote =	{Keywords: dynamic algorithms, maximum depth}
}

Search Results

Documents authored by Yang, Xiongxin

Dynamic Maximum Depth of Geometric Objects

Abstract

Cite as

Thanks for your feedback!

Could not send message