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- W2898811060 abstract "In this paper we present two graph algorithms in the Broadcast Congested Clique model. In this model, there are n players, which communicate in synchronous rounds. Each player represents a single node of the input graph; initially each player knows the set of edges incident to his node. In each round of communication each node can broadcast a single b–bit message to all other nodes; usually $$b in {mathcal {O}}(log n)$$ . The goal is to compute some function of the input graph. The first result we present is the first sub-logarithmic deterministic algorithm finding a maximal spanning forest of an n node graph in the Broadcast Congested Clique, which requires only $${mathcal {O}}(log n / log log n)$$ rounds. The second result is a randomized $$1 + epsilon $$ approximation algorithm finding the minimum cut of an n node graph, which requires only $${mathcal {O}}(log n)$$ maximal spanning forest computations. In the Broadcast Congested Clique this approach, combined with the new maximal spanning forest algorithm, yields an $${mathcal {O}}(log ^2 n / log log n)$$ round algorithm. Additionally, it may be applied to different models, i.e. in the multi-pass semi-streaming model it allows to reduce required memory by $$varTheta (log n)$$ factor, with only $${mathcal {O}}(log ^* n)$$ passes over the data stream." @default.
- W2898811060 created "2018-11-09" @default.
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- W2898811060 date "2018-01-01" @default.
- W2898811060 modified "2023-10-17" @default.
- W2898811060 title "Connectivity and Minimum Cut Approximation in the Broadcast Congested Clique" @default.
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- W2898811060 doi "https://doi.org/10.1007/978-3-030-01325-7_28" @default.
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