Abstract
We consider the problem of designing deterministic graph algorithms for the model of Massively Parallel Computation (MPC) that improve with the sparsity of the input graph, as measured by the standard notion of arboricity. For the problems of maximal independent set (MIS), maximal matching (MM), and vertex coloring, we improve the state of the art as follows. Let λ denote the arboricity of the n-node input graph with maximum degree Δ.
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