Fixed Parameter Algorithms for one-sided crossing minimization Revisited

We exhibit a small problem kernel for the problem onesided crossing minimization which plays an important role in graph drawing algorithms based on the Sugiyama layering approach. Moreover, we improve on the search tree algorithm developed in [5] and derive an O(1.4656k + kn) algorithm for this problem, where k upperbounds the number of tolerated crossings of straight lines involved in the drawings of an n-vertex graph. Relations of this graph-drawing problem to the algebraic problem of finding a weighted linear extension of an ordering similar to [7] are exhibited.