Maintaining bridge-connected and biconnected components on-line Jeffery Westbrook Robert E. Tarjan Article

Received: 01 September 1989 Revised: 08 June 1990 DOI :
10.1007/BF01758773

Cite this article as: Westbrook, J. & Tarjan, R.E. Algorithmica (1992) 7: 433. doi:10.1007/BF01758773
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 (m α(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 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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Authors and Affiliations Jeffery Westbrook Robert E. Tarjan 1. Department of Computer Science Yale University New Haven USA 2. Department of Computer Science Princeton University Princeton USA 3. NEC Research Institute Princeton USA