Faster algorithms for edge connectivity via random 2-out contractions
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Faster algorithms for edge connectivity via random 2-out contractions. / Ghaffari, Mohsen; Nowicki, Krzysztof; Thorup, Mikkel.
31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020. ed. / Shuchi Chawla. Association for Computing Machinery, 2020. p. 1260-1279.Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - Faster algorithms for edge connectivity via random 2-out contractions
AU - Ghaffari, Mohsen
AU - Nowicki, Krzysztof
AU - Thorup, Mikkel
PY - 2020
Y1 - 2020
N2 - We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We demonstrate the power of our new approach by obtaining better algorithms for sequential, distributed, and parallel models of computation. Our end results include the following randomized algorithms for computing edge connectivity, with high probability1: • Two sequential algorithms with complexities O(m log n) and O(m + n log3 n). These improve on a long line of developments including a celebrated O(m log3 n) algorithm of Karger [STOC'96] and the state of the art O(m log2 n(log log n)2) algorithm of Henzinger et al. [SODA'17]. Moreover, our O(m + n log3 n) algorithm is optimal when m = Ω(n log3 n). • An Õ(n0.8D0.2 + n0.9) round distributed algorithm, where D denotes the graph diameter. This improves substantially on a recent breakthrough of Daga et al.[STOC'19], which achieved a round complexity of Õ(n1−1/353D1/353 + n1−1/706), hence providing the first sublinear distributed algorithm for exactly computing the edge connectivity. • The first O(1) round algorithm for the massively parallel computation setting with linear memory per machine.
AB - We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We demonstrate the power of our new approach by obtaining better algorithms for sequential, distributed, and parallel models of computation. Our end results include the following randomized algorithms for computing edge connectivity, with high probability1: • Two sequential algorithms with complexities O(m log n) and O(m + n log3 n). These improve on a long line of developments including a celebrated O(m log3 n) algorithm of Karger [STOC'96] and the state of the art O(m log2 n(log log n)2) algorithm of Henzinger et al. [SODA'17]. Moreover, our O(m + n log3 n) algorithm is optimal when m = Ω(n log3 n). • An Õ(n0.8D0.2 + n0.9) round distributed algorithm, where D denotes the graph diameter. This improves substantially on a recent breakthrough of Daga et al.[STOC'19], which achieved a round complexity of Õ(n1−1/353D1/353 + n1−1/706), hence providing the first sublinear distributed algorithm for exactly computing the edge connectivity. • The first O(1) round algorithm for the massively parallel computation setting with linear memory per machine.
UR - http://www.scopus.com/inward/record.url?scp=85084036820&partnerID=8YFLogxK
U2 - 10.1137/1.9781611975994.77
DO - 10.1137/1.9781611975994.77
M3 - Article in proceedings
AN - SCOPUS:85084036820
SP - 1260
EP - 1279
BT - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
A2 - Chawla, Shuchi
PB - Association for Computing Machinery
T2 - 31st Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2020
Y2 - 5 January 2020 through 8 January 2020
ER -
ID: 258499831