A Fast and Simple Subexponential Fixed Parameter Algorithm for One-Sided Crossing Minimization - Kobayashi, Yasuaki; Tamaki, Hisao (Algorithmica, 2015)
We give a subexponential fixed parameter algorithm for one-sided crossing minimization. It runs in time, where n is the number of vertices of the given graph and parameter k is the number of crossings. The exponent of in this bound is asymptotically optimal assuming the Exponential Time Hypothesis and the previously best known algorithm runs in time. We achieve this significant improvement by the use of a certain interval graph naturally associated with the problem instance and a simple dynamic program on this interval graph. The linear dependency on n is also achieved through the use of this interval graph.