  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. 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.
