TY - GEN

T1 - Connected Components on a PRAM in Log Diameter Time

AU - Liu, Sixue Cliff

AU - Tarjan, Robert E.

AU - Zhong, Peilin

N1 - Publisher Copyright:
© 2020 ACM.

PY - 2020/7/6

Y1 - 2020/7/6

N2 - We present an O(log d + log logm/n n)-time randomized PRAM algorithm for computing the connected components of an n-vertex, m-edge undirected graph with maximum component diameter d. The algorithm runs on an ARBITRARY CRCW (concurrent-read, concurrent-write with arbitrary write resolution) PRAM using O(m) processors. The time bound holds with good probability. Our algorithm is based on the breakthrough results of Andoni et al. [FOCS'18] and Behnezhad et al. [FOCS'19]. Their algorithms run on the more powerful MPC model and rely on sorting and computing prefix sums in O(1) time, tasks that take ω(log n / log log n) time on a CRCW PRAM with poly(n) processors. Our simpler algorithm uses limited-collision hashing and does not sort or do prefix sums. It matches the time and space bounds of the algorithm of Behnezhad et al., who improved the time bound of Andoni et al. It is widely believed that the larger private memory per processor and unbounded local computation of the MPC model admit algorithms faster than that on a PRAM. Our result suggests that such additional power might not be necessary, at least for fundamental graph problems like connected components and spanning forest.

AB - We present an O(log d + log logm/n n)-time randomized PRAM algorithm for computing the connected components of an n-vertex, m-edge undirected graph with maximum component diameter d. The algorithm runs on an ARBITRARY CRCW (concurrent-read, concurrent-write with arbitrary write resolution) PRAM using O(m) processors. The time bound holds with good probability. Our algorithm is based on the breakthrough results of Andoni et al. [FOCS'18] and Behnezhad et al. [FOCS'19]. Their algorithms run on the more powerful MPC model and rely on sorting and computing prefix sums in O(1) time, tasks that take ω(log n / log log n) time on a CRCW PRAM with poly(n) processors. Our simpler algorithm uses limited-collision hashing and does not sort or do prefix sums. It matches the time and space bounds of the algorithm of Behnezhad et al., who improved the time bound of Andoni et al. It is widely believed that the larger private memory per processor and unbounded local computation of the MPC model admit algorithms faster than that on a PRAM. Our result suggests that such additional power might not be necessary, at least for fundamental graph problems like connected components and spanning forest.

KW - PRAM

KW - connected components

KW - hashing

UR - http://www.scopus.com/inward/record.url?scp=85088639095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85088639095&partnerID=8YFLogxK

U2 - 10.1145/3350755.3400249

DO - 10.1145/3350755.3400249

M3 - Conference contribution

AN - SCOPUS:85088639095

T3 - Annual ACM Symposium on Parallelism in Algorithms and Architectures

SP - 359

EP - 369

BT - SPAA 2020 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures

PB - Association for Computing Machinery

T2 - 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020

Y2 - 15 July 2020 through 17 July 2020

ER -