Engineering A Ptas For Minimum Feedback Vertex Set In Planar Graphs

We investigate the practicality of approximation schemes for optimization problems in planar graphs based on balanced separators. The first polynomial-time approximation schemes (PTASes) for problems in planar graphs were based on balanced separators, wherein graphs are recursively decomposed into small enough pieces in which optimal solutions can be found by brute force or other methods. However, this technique was supplanted by the more modern and (theoretically) more efficient approach of decomposing a planar graph into graphs of bounded treewidth, in which optimal solutions are found by dynamic programming. While the latter approach has been tested experimentally, the former approach has not.To test the separator-based method, we examine the minimum feed-back vertex set (FVS) problem in planar graphs. We propose a new, simple O(n log n)-time approximation scheme for FVS using balanced separators and a linear kernel. The linear kernel reduces the size of the graph to be linear in the size of the optimal solution. In doing so, we correct a reduction rule in Bonamy and Kowalik's linear kernel [11] for FVS. We implemented this PTAS and evaluated its performance on large synthetic and real-world planar graphs. Unlike earlier planar PTAS engineering results [8,36], our implementation guarantees the theoretical error bounds on all tested graphs.