Dynamic connectivity is one of the most fundamental problems in dynamic graphalgorithms. We present a randomized Las Vegas dynamic connectivity datastructure 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 thecell probe lower bounds of Patrascu and Demaine (2006) and Patrascu and Thorup(2011). 
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                            Random matrices with log-range correlations, and log-Sobolev inequalities
                        
                    - Award ID(s):
- 1800733
- PAR ID:
- 10332857
- Date Published:
- Journal Name:
- Annales Mathématiques Blaise Pascal
- Volume:
- 27
- Issue:
- 2
- ISSN:
- 2118-7436
- Page Range / eLocation ID:
- 207 to 232
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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