A 1-PLS of cost p implies a t-PLS of cost O(ceil(p/t)) up to log n factors in general graphs and O(ceil(p/t) + log n) in fixed minor-free graphs.
Klein, Serge A
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Near-Resolution of the Tradeoff Conjecture in Distributed Proof Labeling Schemes
A 1-PLS of cost p implies a t-PLS of cost O(ceil(p/t)) up to log n factors in general graphs and O(ceil(p/t) + log n) in fixed minor-free graphs.