Fully Dynamic Connectivity in $O(\log n(\log\log n)^2)$ Amortized Expected Time

Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a randomized Las Vegas dynamic connectivity data structure with $O(\log n(\log\log n)^2)$ amortized expected update time and $O(\log n/\log\log\log n)$ worst case query time, which comes very close t...

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Bibliographic Details
Published in:	TheoretiCS Vol. 2
Main Authors:	Huang, Shang-En, Huang, Dawei, Kopelowitz, Tsvi, Pettie, Seth, Thorup, Mikkel
Format:	Journal Article
Language:	English
Published:	TheoretiCS Foundation e.V 02.05.2023
Subjects:	computer science - data structures and algorithms
ISSN:	2751-4838, 2751-4838
Online Access:	Get full text
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Summary:	Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a randomized Las Vegas dynamic connectivity data structure with $O(\log n(\log\log n)^2)$ amortized expected update time and $O(\log n/\log\log\log n)$ worst case query time, which comes very close to the cell probe lower bounds of Patrascu and Demaine (2006) and Patrascu and Thorup (2011).
ISSN:	2751-4838 2751-4838
DOI:	10.46298/theoretics.23.6