Two-Layer Planarization Parameterized by Feedback Edge Set

Given an undirected graph G and an integer k ≥ 0, the NPhard 2-Layer Planarization problem asks whether G can be transformed into a forest of caterpillar trees by removing at most k edges. Since transforming G into a forest of caterpillar trees requires breaking every cycle, the size f of a minimum feedback edge set is a natural parameter with f ≤ k. We improve on previous fixed-parameter tractability results with respect to k by presenting a problem kernel with O(f) vertices and edges and a new search-tree based algorithm, both with about the same worst-case bounds for f as the previous results for k, although we expect f to be smaller than k for a wide range of input instances.