# Applications of Path Compression on Balanced Trees

@article{Tarjan1979ApplicationsOP,
title={Applications of Path Compression on Balanced Trees},
author={Robert E. Tarjan},
journal={J. ACM},
year={1979},
volume={26},
pages={690-715}
}
• R. Tarjan
• Published 1 October 1979
• Computer Science
• J. ACM
We devise a method for computing functions defined on paths in trees. The method is based on tree manipulation techniques first used for efficiently representing equivalence relations. It has an almost-linear running time. We apply the method to give O(m $\alpha$(m,n)) algorithms for two problems. A. Verifying a minimum spanning tree in an undirected graph (best previous bound: O(m log log n) ). B. Finding dominators in a directed graph (best previous bound: O(n log n + m) ). Here n is the…
308 Citations

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