Abstract
Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a new randomized dynamic connectivity structure with O(log n(log log n)2) amortized expected update time and O(log n/log log log n) query time, which comes within an O((log log n)2) factor of a lower bound due to Pǎtrascu and Demaine. The new structure is based on a dynamic connectivity algorithm proposed by Thorup in an extended abstract at STOC 2000, which left out some important details.
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