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

Dawei Huang; Mikkel Thorup; Seth Pettie; Shang-En Huang; Tsvi Kopelowitz

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

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arxiv 1609.05867 v4 pith:DHXH6LKZ submitted 2016-09-19 cs.DS

Shang-En Huang , Dawei Huang , Tsvi Kopelowitz , Seth Pettie , Mikkel Thorup This is my paper

classification cs.DS

keywords dynamicconnectivitytimeamortizedexpectedpatrascualgorithmsbounds

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abstract

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).

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