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We study dynamic graph algorithms in the Massively Parallel Computationmodel, which was inspired by practical data processing systems. Our goal is toprovide algorithms that can efficiently handle large batches of edge insertionsand deletions.  We show algorithms that require fewer rounds to update a solution to problemssuch as Minimum Spanning Forest, 2-Edge Connected Components, and MaximalMatching than would be required by their static counterparts to compute it fromscratch. They work in the most restrictive memory regime, in which local memoryper machine is strongly sublinear in the number of graph vertices. Improving onthe size of the batch they can handle efficiently would improve on the roundcomplexity of known static algorithms on sparse graphs.  Our algorithms can process batches of updates of size $\Theta(S)$, forMinimum Spanning Forest and 2-Edge Connected Components, and$\Theta(S^{1-\varepsilon})$, for Maximal Matching, in $O(1)$ rounds, where $S$is the local memory of a single machine.

Dynamic Graph Algorithms with Batch Updates in the Massively Parallel Computation Model