In the left-regular random model, greedy for maximum coverage has expected approximation ratio strictly above 1-1/e for all parameters, approaches 1 under two conditions for large graphs, but is at most 0.94 in some regimes.
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On the Average-Case Performance of Greedy for Maximum Coverage
In the left-regular random model, greedy for maximum coverage has expected approximation ratio strictly above 1-1/e for all parameters, approaches 1 under two conditions for large graphs, but is at most 0.94 in some regimes.