Two-Layer planarization parameterized by feedback edge set

Authors:
Johannes Uhlmann;Mathias Weller
Affiliations:
Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany;Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany
Venue:
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Year:
2010

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Abstract

Given an undirected graph G and an integer k≥0, the NP-hard 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.