A new analysis of an existing local algorithm yields O(log lambda)-round LOCAL and O(sqrt(log lambda) log log lambda)-round sublinear-space MPC algorithms for (1+epsilon)-approximate allocation in graphs of arboricity lambda.
Balseiro, Haihao Lu, and Vahab Mirrokni
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Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
A new analysis of an existing local algorithm yields O(log lambda)-round LOCAL and O(sqrt(log lambda) log log lambda)-round sublinear-space MPC algorithms for (1+epsilon)-approximate allocation in graphs of arboricity lambda.