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
- NSF-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