Fixed parameter algorithms for one-sided crossing minimization revisited

We exhibit a small problem kernel for the one-sided crossing minimization problem. This problem plays an important role in graph drawing algorithms based on the Sugiyama layering approach. Moreover, we improve on the search tree algorithm developed in [V. Dujmović, S. Whitesides, An efficient fixed parameter tractable algorithm for 1-sided crossing minimization, Algorithmica 40 (2004) 15–31] and derive an O(k1.4656+kn2)O(1.4656k+kn2) algorithm for this problem, where k upperbounds the number of tolerated edge crossings in the drawings of an n-vertex graph.