By Topic

Fully dynamic biconnectivity and transitive closure

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Henzinger, M.R. ; Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA ; King, V.

This paper presents an algorithm for the fully dynamic biconnectivity problem whose running time is exponentially faster than all previously known solutions. It is the first dynamic algorithm that answers biconnectivity queries in time O(log2n) in a n-node graph and can be updated after an edge insertion or deletion in polylogarithmic time. Our algorithm is a Las-Vegas style randomized algorithm with the update time amortized update time O(log4n). Only recently the best deterministic result for this problem was improved to O(√nlog2n). We also give the first fully dynamic and a novel deletions-only transitive closure (i.e. directed connectivity) algorithms. These are randomized Monte Carlo algorithms. Let n be the number of nodes in the graph and let mˆ be the average number of edges in the graph during the whole update sequence: The fully dynamic algorithms achieve (1) query time O(n/logn) and update time O(mˆ√nlog2n+n); or (2) query time O(n/logn) and update time O(nmˆμ-1)log2n=O(nmˆ0.58 log2n), where μ is the exponent for boolean matrix multiplication (currently μ=2.38). The deletions-only algorithm answers queries in time O(n/logn). Its amortized update time is O(nlog 2n)

Published in:

Foundations of Computer Science, 1995. Proceedings., 36th Annual Symposium on

Date of Conference:

23-25 Oct 1995