We present the first near-linear work and poly-logarithmic depth algorithm
for computing a minimum cut in a graph, while previous parallel algorithms with
poly-logarithmic depth required at least quadratic work in the number of
vertices. In a graph with n vertices and m edges, our algorithm computes
the correct result with high probability in O(mlog4n) work and
O(log3n) depth. This result is obtained by parallelizing a data
structure that aggregates weights along paths in a tree and by exploiting the
connection between minimum cuts and approximate maximum packings of spanning
trees. In addition, our algorithm improves upon bounds on the number of cache
misses incurred to compute a minimum cut