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Dynamic Streaming Algorithms for Geometric Independent Set

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Názov: Dynamic Streaming Algorithms for Geometric Independent Set
Autori: Chan, Timothy M., Yu, Yuancheng
Prispievatelia: Timothy M. Chan and Yuancheng Yu
Informácie o vydavateľovi: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2025.
Rok vydania: 2025
Predmety: ddc:004, Dynamic Streaming Algorithms, Geometric Independent Set
Popis: 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.
Druh dokumentu: Conference object
Popis súboru: application/pdf
Jazyk: English
DOI: 10.4230/lipics.wads.2025.17
Prístupová URL adresa: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.17
Rights: CC BY
Prístupové číslo: edsair.od......1814..b6a610fa9ea5343386d285965f57f47f
Databáza: OpenAIRE
Popis
Abstrakt: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.
DOI:10.4230/lipics.wads.2025.17