An Alternative Method to Crossing Minimization on Hierarchical Graphs
SIAM Journal on Optimization
A Fixed-Parameter Approach to Two-Layer Planarization
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
On the Parameterized Complexity of Layered Graph Drawing
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
Parameterized Complexity
Approximation and fixed-parameter algorithms for consecutive ones submatrix problems
Journal of Computer and System Sciences
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A bipartite graph is biplanar if the vertices can be placed on two parallel lines in the plane such that there are no edge crossings when edges are drawn as straight-line segments. We study two problems:2-Layer Planarization: can k edges be deleted from a given graph G so that the remaining graph is biplanar? 1-Layer Planarization: same question, but the order of the vertices on one layer is fixed. Improving on earlier works of Dujmović et al. [4], we solve the 2-Layer Planarization problem in $\mathcal{O}(k^{2}\cdot 5.1926^{k} +|G|)$ time and the 1-Layer Planarization problem in $\mathcal{O}(k^{3} \cdot 2.5616^{k} + |G|^{2})$ time. Moreover, we derive a small problem kernel for 1-Layer Planarization.