We present a deterministic dynamic connectivity data structure for undirected graphs with worst case update time O(sqrt{(n(log(log(n)))^2)/log(n)}) and constant query time. This improves on the previous best deterministic worst case algorithm of Frederickson (SIAM J. Comput., 1985) and Eppstein Galil, Italiano, and Nissenzweig (J. ACM, 1997), which had update time O(sqrt{n}). All other algorithms for dynamic connectivity are either randomized (Monte Carlo) or have only amortized performance guarantees.
@InProceedings{kejlbergrasmussen_et_al:LIPIcs.ESA.2016.53, author = {Kejlberg-Rasmussen, Casper and Kopelowitz, Tsvi and Pettie, Seth and Thorup, Mikkel}, title = {{Faster Worst Case Deterministic Dynamic Connectivity}}, booktitle = {24th Annual European Symposium on Algorithms (ESA 2016)}, pages = {53:1--53:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-015-6}, ISSN = {1868-8969}, year = {2016}, volume = {57}, editor = {Sankowski, Piotr and Zaroliagis, Christos}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.53}, URN = {urn:nbn:de:0030-drops-63953}, doi = {10.4230/LIPIcs.ESA.2016.53}, annote = {Keywords: dynamic graph, spanning tree} }
Feedback for Dagstuhl Publishing