Abstract

We prove that there is no fpt-algorithm that can approximate the dominating set problem with any constant ratio, unless FPT = W[1]. Our hardness reduction is built on the second author's recent W[1]-hardness proof of the biclique problem [25]. This yields, among other things, a proof without the PCP machinery that the classical dominating set problem has no polynomial time constant approximation under the exponential time hypothesis.

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