Abstract
Since Min-CDS is NP-hard, approximation algorithm design becomes an important issue in study of CDS. What is the complexity of approximation for Min-CDS? Guha and Khuller [62] showed that Min-CDS has no polynomial-time (ρ lnn)-approximation for 0 < ρ < 1 unless \(NP \subseteq DTIME({n}^{O(\log \log n)})\) where n is the number of vertices in input graph. Moreover, they designed a 2-stage greedy algorithm with performance ratio 3 + lnδ where δ is the maximum vertex degree of input graph. The effort on improvement of this 2-stage greedy algorithm encounted an essential difficulty on analysis of greed approximation.
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