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Achieving a near-optimal \( \tilde{O}(D) \)-rounds approximation for Maximum \( st \)-Flow in undirected planar graphs could revolutionize distributed optimization strategies in complex networks.
Achieving $O(\log n)$ approximation of APSP in constant rounds could revolutionize efficiency in multiparty computation settings.
A surprisingly simple weight-transfer trick unlocks a near-optimal deterministic algorithm for finding balanced separators in planar graphs, potentially derandomizing a suite of distributed algorithms for problems like shortest paths and max-flow.