Parallel Minimum Cuts in Near-linear Work and Low Depth

We present the first near-linear work and poly-logarithmic depth algorithm for computing a minimum cut in an undirected graph. Previous parallel algorithms with required at least quadratic number of vertices. In graph n vertices m edges, our randomized computes high probability O ( log 4 ) (log 3 depth. This result is obtained by parallelizing data structure that aggregates weights along paths tree, addition exploiting connection between cuts approximate maximum packings spanning trees. addition, improves upon bounds on cache misses incurred to compute cut.