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- W4287996923 abstract "In this paper, we show that the Minimum Spanning Tree problem can be solved emph{deterministically}, in $mathcal{O}(1)$ rounds of the $mathsf{Congested}$ $mathsf{Clique}$ model. In the $mathsf{Congested}$ $mathsf{Clique}$ 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 $mathcal{O}(log n)$ bit messages. The studies of this model began with the MST problem: in the paper by Lotker et al.[SPAA'03, SICOMP'05] that defines the $mathsf{Congested}$ $mathsf{Clique}$ model the authors give a deterministic $mathcal{O}(log log n)$ round algorithm that improved over a trivial $mathcal{O}(log n)$ round adaptation of Borr{u}vka's algorithm. There was a sequence of gradual improvements to this result: an $mathcal{O}(log log log n)$ round algorithm by Hegeman et al. [PODC'15], an $mathcal{O}(log^* n)$ round algorithm by Ghaffari and Parter, [PODC'16] and an $mathcal{O}(1)$ round algorithm by Jurdzi'nski and Nowicki, [SODA'18], but all those algorithms were randomized, which left the question about the existence of any deterministic $o(log log n)$ round algorithms for the Minimum Spanning Tree problem open. Our result resolves this question and establishes that $mathcal{O}(1)$ rounds is enough to solve the MST problem in the $mathsf{Congested}$ $mathsf{Clique}$ model, even if we are not allowed to use any randomness. Furthermore, the amount of communication needed by the algorithm makes it applicable to some variants of the $mathsf{MPC}$ model." @default.
- W4287996923 created "2022-07-26" @default.
- W4287996923 creator A5013781866 @default.
- W4287996923 date "2019-12-09" @default.
- W4287996923 modified "2023-09-24" @default.
- W4287996923 title "A Deterministic Algorithm for the MST Problem in Constant Rounds of Congested Clique" @default.
- W4287996923 doi "https://doi.org/10.48550/arxiv.1912.04239" @default.
- W4287996923 hasPublicationYear "2019" @default.
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