A batch-dynamic massively parallel algorithm maintains undirected graph connectivity in a constant number of communication rounds with near-linear communication per batch, alongside a P-completeness lower bound for adaptive connectivity.
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Parallel Batch-Dynamic Graphs: Algorithms and Lower Bounds
A batch-dynamic massively parallel algorithm maintains undirected graph connectivity in a constant number of communication rounds with near-linear communication per batch, alongside a P-completeness lower bound for adaptive connectivity.