TY - GEN

T1 - Massively Parallel Computation in a Heterogeneous Regime

AU - Fischer, Orr

AU - Horowitz, Adi

AU - Oshman, Rotem

N1 - Publisher Copyright:
© 2022 ACM.

PY - 2022/7/20

Y1 - 2022/7/20

N2 - Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The sublinear regime is the most desirable in practice, but conditional hardness results point towards its limitations. In this work we study a heterogeneous model, where the memory of the machines varies in size. We focus mostly on the heterogeneous setting created by adding a single near-linear machine to the sublinear MPC regime, and show that even a single large machine suffices to circumvent most of the conditional hardness results for the sublinear regime: for graphs with n vertices and m edges, we give (a) an MST algorithm that runs in O(łogłog(m/n)) rounds; (b) an algorithm that constructs an O(k)-spanner of size O(n^1+1/k ) in O(1) rounds; and (c) a maximal-matching algorithm that runs in O(g łog(m/n) łogłog(m/n)) rounds. We also observe that the best known near-linear MPC algorithms for several other graph problems which are conjectured to be hard in the sublinear regime (minimum cut, maximal independent set, and vertex coloring) can easily be transformed to work in the heterogeneous MPC model with a single near-linear machine, while retaining their original round complexity in the near-linear regime. If the large machine is allowed to have superlinear memory, all of the problems above can be solved in O(1) rounds.

AB - Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The sublinear regime is the most desirable in practice, but conditional hardness results point towards its limitations. In this work we study a heterogeneous model, where the memory of the machines varies in size. We focus mostly on the heterogeneous setting created by adding a single near-linear machine to the sublinear MPC regime, and show that even a single large machine suffices to circumvent most of the conditional hardness results for the sublinear regime: for graphs with n vertices and m edges, we give (a) an MST algorithm that runs in O(łogłog(m/n)) rounds; (b) an algorithm that constructs an O(k)-spanner of size O(n^1+1/k ) in O(1) rounds; and (c) a maximal-matching algorithm that runs in O(g łog(m/n) łogłog(m/n)) rounds. We also observe that the best known near-linear MPC algorithms for several other graph problems which are conjectured to be hard in the sublinear regime (minimum cut, maximal independent set, and vertex coloring) can easily be transformed to work in the heterogeneous MPC model with a single near-linear machine, while retaining their original round complexity in the near-linear regime. If the large machine is allowed to have superlinear memory, all of the problems above can be solved in O(1) rounds.

KW - heterogeneous memory regime

KW - massively parallel computation

UR - http://www.scopus.com/inward/record.url?scp=85135340076&partnerID=8YFLogxK

U2 - 10.1145/3519270.3538450

DO - 10.1145/3519270.3538450

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AN - SCOPUS:85135340076

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 345

EP - 355

BT - PODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

PB - Association for Computing Machinery

T2 - 41st ACM Symposium on Principles of Distributed Computing, PODC 2022

Y2 - 25 July 2022 through 29 July 2022

ER -