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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Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension
- Award ID(s):
- 1565352
- NSF-PAR ID:
- 10230202
- Date Published:
- Journal Name:
- Journal of the American Mathematical Society
- Volume:
- 30
- Issue:
- 4
- ISSN:
- 0894-0347
- Page Range / eLocation ID:
- 959 to 1021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation