4 research outputs found
Work-Optimal Parallel Minimum Cuts for Non-Sparse Graphs
We present the first work-optimal polylogarithmic-depth parallel algorithm
for the minimum cut problem on non-sparse graphs. For
for any constant , our algorithm requires work and
depth and succeeds with high probability. Its work matches the
best runtime for sequential algorithms [MN STOC 2020, GMW SOSA
2021]. This improves the previous best work by Geissmann and Gianinazzi [SPAA
2018] by 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.Comment: Updates on this version: Minor corrections for the previous and our
resul
Parallel searching in generalized Monge arrays with applications
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