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 poly-logarithmic depth required at least quadratic work in the number of vertices.
In a graph with
n
vertices and
m
edges, our randomized algorithm computes the minimum cut with high probability in
O
(
m
log
4
n
) work and
O
(log
3
n
) depth. This result is obtained by parallelizing a data structure that aggregates weights along paths in a tree, in addition 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.
Work-Optimal Parallel Minimum Cuts for Non-Sparse Graphs
