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Faster Worst Case Deterministic Dynamic Connectivity

Authors Casper Kejlberg-Rasmussen, Tsvi Kopelowitz, Seth Pettie, Mikkel Thorup

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Casper Kejlberg-Rasmussen
Tsvi Kopelowitz
Seth Pettie
Mikkel Thorup

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Casper Kejlberg-Rasmussen, Tsvi Kopelowitz, Seth Pettie, and Mikkel Thorup. Faster Worst Case Deterministic Dynamic Connectivity. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ESA.2016.53

Abstract

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.

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Keywords
  • dynamic graph
  • spanning tree

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