Article

Algorithmica

, Volume 7, Issue 1, pp 433-464

First online:

Maintaining bridge-connected and biconnected components on-line

  • Jeffery WestbrookAffiliated withDepartment of Computer Science, Yale University
  • , Robert E. TarjanAffiliated withDepartment of Computer Science, Princeton UniversityNEC Research Institute

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Abstract

We consider the twin problems of maintaining the bridge-connected components and the biconnected components of a dynamic undirected graph. The allowed changes to the graph are vertex and edge insertions. We give an algorithm for each problem. With simple data structures, each algorithm runs inO(n logn +m) time, wheren is the number of vertices andm is the number of operations. We develop a modified version of the dynamic trees of Sleator and Tarjan that is suitable for efficient recursive algorithms, and use it to reduce the running time of the algorithms for both problems toO(mα(m,n)), where α is a functional inverse of Ackermann's function. This time bound is optimal. All of the algorithms useO(n) space.

Key words

On-line algorithms Graph algorithms Graph connectivity Dynamic trees Data structures