  We present two algorithms for the minimum feedback vertex set problem in
planar graphs: an $O(n \log n)$ PTAS using a linear kernel and balanced
separator, and a heuristic algorithm using kernelization and local search. We
implemented these algorithms and compared their performance with Becker and
Geiger's 2-approximation algorithm. We observe that while our PTAS is
competitive with the 2-approximation algorithm on large planar graphs, its
running time is much longer. And our heuristic algorithm can outperform the
2-approximation algorithm on most large planar graphs and provide a trade-off
between running time and solution quality, i.e. a "PTAS behavior".
