  We give an algorithm that for an input n-vertex graph G and integer k>0, in
time 2^[O(k)]n either outputs that the treewidth of G is larger than k, or
gives a tree decomposition of G of width at most 5k+4. This is the first
algorithm providing a constant factor approximation for treewidth which runs in
time single-exponential in k and linear in n. Treewidth based computations are
subroutines of numerous algorithms. Our algorithm can be used to speed up many
such algorithms to work in time which is single-exponential in the treewidth
and linear in the input size.
