  Prize-Collecting TSP is a variant of the traveling salesperson problem where
one may drop vertices from the tour at the cost of vertex-dependent penalties.
The quality of a solution is then measured by adding the length of the tour and
the sum of all penalties of vertices that are not visited. We present a
polynomial-time approximation algorithm with an approximation guarantee
slightly below $1.6$, where the guarantee is with respect to the natural linear
programming relaxation of the problem. This improves upon the previous
best-known approximation ratio of $1.774$. Our approach is based on a known
decomposition for solutions of this linear relaxation into rooted trees. Our
algorithm takes a tree from this decomposition and then performs a pruning step
before doing parity correction on the remainder. Using a simple analysis, we
bound the approximation guarantee of the proposed algorithm by $(1+\sqrt{5})/2
\approx 1.618$, the golden ratio. With some additional technical care we
further improve it to $1.599$.
