A "k"-tuple dominating set is a set of vertices such that each vertex in the graph has at least "k" neighbors in the set. An (1+log n)-approximation of a minimum "k"-tuple dominating set can be found in polynomial time. Similarly, a "k"-dominating set is a set of vertices such that each vertex not in the set has at least "k" neighbors in the set. While every graph admits a "k"-dominating set, only graphs with minimum degree "k" − 1 admit a "k"-tuple dominating set. However, even if the graph admits k-tuple dominating set, a minimum "k"-tuple dominating set can be nearly "k" times as large as a minimum "k"-dominating set for the same graph; An (1.7 + log Δ)-approximation of a minimum "k"-dominating set can be found in polynomial time as well.