Abstract
We consider the problem of testing a digraph G = (V,E) for upward planarity. In particular we present two fixed-parameter tractable algorithms for testing the upward planarity of G. Let n = |V|, let t be the number of triconnected components of G, and let c be the number of cut-vertices of G. The first upward planarity testing algorithm we present runs in O(2t · t! · n 2)–time. The previously known best result is an O(t! · 8t · n 3 + 23·2 c · t 3·2 c · t! · 8t · n)-time algorithm by Chan. We use the kernelisation technique to develop a second upward planarity testing algorithm which runs in O(n 2 + k 4(2k + 1)!) time, where k = |E| – |V|. We also define a class of non upward planar digraphs.
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Healy, P., Lynch, K. (2005). Fixed-Parameter Tractable Algorithms for Testing Upward Planarity. 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_23
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DOI: https://doi.org/10.1007/978-3-540-30577-4_23
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