Near-optimal dominating sets in dense random graphs in polynomial expected time
The probability of existence of dominating sets of size less than log n tends to zero as n tends to infinity.
Dominating sets of size [log n] exist almost surely.
We provide two algorithms which construct small dominating sets in G n, 1/2 run in O (n alog n) time (on the average and also with high probability). Our algorithms almost surely construct a dominating set of size at most (1+ε) log n, for any fixed ε > 0.
Our results extend to the case Gn,p with p fixed to any constant < 1.
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