The minimum k-tuple domination problem can be approximated within ln(Δ+1)+1 and the k-domination ratio improves beyond the prior ln(2Δ)+1 bound.
Feige, A threshold of lnnfor approximation set cover.Journal of ACM45(4) (1998) 634–652
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Approximation algorithms and ratios for multiple domination in graphs
The minimum k-tuple domination problem can be approximated within ln(Δ+1)+1 and the k-domination ratio improves beyond the prior ln(2Δ)+1 bound.