Work-Optimal Parallel Minimum Cuts for Non-Sparse Graphs

02/12/2021
by   Andrés López-Martínez, et al.
0

We present the first work-optimal polylogarithmic-depth parallel algorithm for the minimum cut problem on non-sparse graphs. For m≥ n^1+ϵ for any constant ϵ>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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/10/2021

Parallel Minimum Cuts in O(m log^2(n)) Work and Low Depth

We present an O(m log^2(n)) work, O(polylog(n)) depth parallel algorithm...
research
07/25/2018

Parallel Minimum Cuts in Near-linear Work and Low Depth

We present the first near-linear work and poly-logritharithmic depth alg...
research
09/20/2021

Parallel Algorithms for Finding Large Cliques in Sparse Graphs

We present a parallel k-clique listing algorithm with improved work boun...
research
07/19/2023

Dynamic constant time parallel graph algorithms with sub-linear work

The paper proposes dynamic parallel algorithms for connectivity and bipa...
research
04/19/2023

Nearly Work-Efficient Parallel DFS in Undirected Graphs

We present the first parallel depth-first search algorithm for undirecte...
research
11/17/2020

Ultrasparse Ultrasparsifiers and Faster Laplacian System Solvers

In this paper we provide an O(m (loglog n)^O(1)log(1/ϵ))-expected time a...
research
02/07/2023

Engineering Shared-Memory Parallel Shuffling to Generate Random Permutations In-Place

Shuffling is the process of rearranging a sequence of elements into a ra...

Please sign up or login with your details

Forgot password? Click here to reset