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This work completely closes the approximation gap between undirected and directed DS in the semi-streaming setting, matching the $(1-\varepsilon)-approximate undirected DS algorithm by Esfandiari, Hajiaghayi, and Woodruff (2016).
This is the first $O(1)$-approximate algorithm for densest subgraph to break the $\Theta(\sqrt{\lg n})$ round-complexity barrier in the sub-linear MPC model and achieves the following round-approximation tradeoffs.
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