Randomized LOCAL algorithm computes 2-ruling sets in O(log log n) rounds w.h.p. on graphs with arboricity O(log log n), nearly matching lower bounds and exponentially improving prior combinations of results.
Pemmaraju, Talal Riaz, and Peter Robinson
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Near-Optimal Distributed 2-Ruling Sets on Graphs with Low Arboricity
Randomized LOCAL algorithm computes 2-ruling sets in O(log log n) rounds w.h.p. on graphs with arboricity O(log log n), nearly matching lower bounds and exponentially improving prior combinations of results.