Parallel Minimum Cuts in Near-linear Work and Low Depth

TL;DR

This paper introduces a groundbreaking parallel algorithm for minimum cuts that operates in near-linear work and low depth, significantly improving efficiency over previous methods and optimizing cache usage.

Contribution

It presents the first near-linear work, poly-logarithmic depth parallel algorithm for minimum cuts, leveraging tree path aggregation and spanning tree packings.

Findings

Achieves $O(m \, \log^4 n)$ work and $O(\log^3 n)$ depth with high probability.

Improves bounds on cache misses during minimum cut computation.

Provides a scalable parallel approach for large graphs.

Abstract

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 $O(m {\log}^4 n)$ work and $O({\log}^3 n)$ depth. This result is obtained by parallelizing a data structure that aggregates weights along paths in a tree 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.