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.
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Research at Princeton University supported in part by National Science Foundation Grant DCR-86-05962 and Office of Naval Research Contract N00014-91-J-1463.
This work was partially done while the author was at the Department of Computer Science, Princeton University, Princeton, NJ 08544, USA.
Communicated by Greg N. Frederickson.
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Westbrook, J., Tarjan, R.E. Maintaining bridge-connected and biconnected components on-line. Algorithmica 7, 433–464 (1992). https://doi.org/10.1007/BF01758773
- On-line algorithms
- Graph algorithms
- Graph connectivity
- Dynamic trees
- Data structures