A faster fixed parameter algorithm for two-layer crossing minimization

We give an algorithm that decides whether the bipartite crossing number of a given graph is at most k. The running time of the algorithm is upper bounded by 2 + n, where n is the number of vertices of the input graph, which improves the previously known algorithm due to Kobayashi et al. (TCS 2014) that runs in 2 log +n time. This result is based on a combinatorial upper bound on the number of two-layer drawings of a connected bipartite graph with a bounded crossing number.