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Parallel minimum Cuts in Near-linear Work and Low Depth

ACM TRANSACTIONS ON PARALLEL COMPUTING 2021年第2期8卷 1–20页

作者： Geissmann, Barbara Gianinazzi, Lukas Swiss Fed Inst Technol Dept Comp Sci Univ Str 6 CAB Zurich Switzerland

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.

关键词： minimum cut graph algorithms minimum path data structure parallel algorithms cache-oblivious algorithms

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Parallel minimum Cuts in Near-linear Work and Low Depth 18

Parallel Minimum Cuts in Near-linear Work and Low Depth

引用

30th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)

作者： Geissmann, Barbara Gianinazzi, Lukas Swiss Fed Inst Technol Dept Comp Sci Zurich Switzerland

ISBN: (纸本)9781450357999

We present the first near-linear work and poly-logritharithmic 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 andm 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.

关键词： minimum Cut Graph Algorithms minimum path data structure Parallel Algorithms Cache-oblivious Algorithms

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