Abstract
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:
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2-Layer Planarization: can k edges be deleted from a given graph G so that the remaining graph is biplanar?
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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.
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Fernau, H. (2005). Two-Layer Planarization: Improving on Parameterized Algorithmics. In: Vojtáš, P., Bieliková, M., Charron-Bost, B., Sýkora, O. (eds) SOFSEM 2005: Theory and Practice of Computer Science. SOFSEM 2005. Lecture Notes in Computer Science, vol 3381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30577-4_17
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DOI: https://doi.org/10.1007/978-3-540-30577-4_17
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