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Dynamic Streaming Algorithms for Geometric Independent Set

Authors Timothy M. Chan , Yuancheng Yu

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Geometric Independent Set
  • Dynamic Streaming Algorithms

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Abstract

We present the first space-efficient, fully dynamic streaming algorithm for computing a constant-factor approximation of the maximum independent set size of n axis-aligned rectangles in two dimensions. For an arbitrarily small constant δ > 0, our algorithm obtains an O((1/δ)²) approximation and requires O(U^δ polylog n) space and update time with high probability, assuming that coordinates are integers bounded by U. We also obtain a similar result for fat objects in any constant dimension. This extends recent non-streaming algorithms by Bhore and Chan from SODA'25, and also greatly extends previous streaming results, which were limited to special types of geometric objects such as one-dimensional intervals and unit disks.

Cite As Get BibTex

Timothy M. Chan and Yuancheng Yu. Dynamic Streaming Algorithms for Geometric Independent Set. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.17

Author Details

Timothy M. Chan
  • Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, IL, USA
Yuancheng Yu
  • Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign, IL, USA

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