A deterministic algorithm for the MST problem in constant rounds of congested clique
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
In this paper we show that the Minimum Spanning Tree problem (MST) can be solved deterministically in O(1) rounds of the Congested Clique model. In the Congested Clique model there are n players that perform computation in synchronous rounds. Each round consist of a phase of local computation and a phase of communication, in which each pair of players is allowed to exchange O(logn) bit messages. The studies of this model began with the MST problem: in the paper by Lotker, Pavlov, Patt-Shamir, and Peleg [SPAA'03, SICOMP'05] that defines the Congested Clique model the authors give a deterministic O(loglogn) round algorithm that improved over a trivial O(logn) round adaptation of Borůvka's algorithm. There was a sequence of gradual improvements to this result: an O(logloglogn) round algorithm by Hegeman, Pandurangan, Pemmaraju, Sardeshmukh, and Scquizzato [PODC'15], an O(log? n) round algorithm by Ghaffari and Parter, [PODC'16] and an O(1) round algorithm by Jurdzi?ski and Nowicki, [SODA'18], but all those algorithms were randomized. Therefore, the question about the existence of any deterministic o(loglogn) round algorithms for the Minimum Spanning Tree problem remains open since the seminal paper by Lotker, Pavlov, Patt-Shamir, and Peleg [SPAA'03, SICOMP'05]. Our result resolves this question and establishes that O(1) rounds is enough to solve the MST problem in the Congested Clique model, even if we are not allowed to use any randomness. Furthermore, the amount of communication needed by the algorithm makes it applicable to a variant of the MPC model using machines with local memory of size O(n).
Original language | English |
---|---|
Title of host publication | STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing |
Editors | Samir Khuller, Virginia Vassilevska Williams |
Publisher | Association for Computing Machinery, Inc. |
Publication date | 2021 |
Pages | 1154-1165 |
ISBN (Electronic) | 9781450380539 |
DOIs | |
Publication status | Published - 2021 |
Event | 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021 |
Conference
Conference | 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 |
---|---|
Land | Italy |
By | Virtual, Online |
Periode | 21/06/2021 → 25/06/2021 |
Sponsor | ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) |
Bibliographical note
Publisher Copyright:
© 2021 ACM.
- Congested Clique, Deterministic Algorithms, Distributed Algorithms, Graph algorithms, MapReduce, Massively Parallel Algorithms, Minimum Spanning Tree, MST, Parallel Algorithms
Research areas
ID: 306691028