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arXiv · 2102.06565

Work-Optimal Parallel Minimum Cuts for Non-Sparse Graphs

Andrés López-Martínez·Sagnik Mukhopadhyay·Danupon Nanongkai
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Abstract

We present the first work-optimal polylogarithmic-depth parallel algorithm for the minimum cut problem on non-sparse graphs. For $m\geq n^{1+\epsilon}$ for any constant $\epsilon>0$, our algorithm requires $O(m \log n)$ work and $O(\log^3 n)$ depth and succeeds with high probability. Its work matches the best $O(m \log n)$ runtime for sequential algorithms [MN STOC 2020, GMW SOSA 2021]. This improves the previous best work by Geissmann and Gianinazzi [SPAA 2018] by $O(\log^3 n)$ factor, while matching the depth of their algorithm. To do this, we design a work-efficient approximation algorithm and parallelize the recent sequential algorithms [MN STOC 2020; GMW SOSA 2021] that exploit a connection between 2-respecting minimum cuts and 2-dimensional orthogonal range searching.

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Andrés López-Martínez, Sagnik Mukhopadhyay, Danupon Nanongkai. 2021-02-12. Work-Optimal Parallel Minimum Cuts for Non-Sparse Graphs. https://arxiv.org/abs/2102.06565

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