Optimal Randomized EREW PRAM Algorithms for Finding Spanning Forests

Shay Halperin*, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present the first randomized O(log n) time and O(m + n) work EREW PRAM algorithm for finding a spanning forest of an undirected graph G = (V, E) with n vertices and m edges. Our algorithm is optimal with respect to time, work, and space. As a consequence we get optimal randomized EREW PRAM algorithms for other basic connectivity problems such as finding a bipartite partition, finding bridges and biconnected components, finding Euler tours in Eulerian graphs, finding an ear decomposition, finding an open ear decomposition, finding a strong orientation, and finding an st-numbering.

Original languageEnglish
Pages (from-to)1-46
Number of pages46
JournalJournal of Algorithms
Issue number1
StatePublished - Apr 2001


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