Abstract
Upward planarity testing, or checking whether a directed graph has a drawing in which no edges cross and all edges point upward, is NP-complete. All of the algorithms for upward planarity testing developed previously focused on special classes of graphs. In this paper we develop a parameterized algorithm for upward planarity testing that can be applied to all graphs and runs in O(f(k)n 3 + g(k,ℓ)n) time, where n is the number of vertices, k is the number of triconnected components, and ℓ is the number of cutvertices. The functions f(k) and g(k,ℓ) are defined as f(k)=k!8k and \(g(k,\ell)=2^{3\cdot 2^\ell}k^{3\cdot 2^\ell} k!8^k\). Thus if the number of triconnected components and the number of cutvertices are small, the problem can be solved relatively quickly, even for a large number of vertices. This is the first parameterized algorithm for upward planarity testing.
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Chan, H. (2004). A Parameterized Algorithm for Upward Planarity Testing. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_16
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DOI: https://doi.org/10.1007/978-3-540-30140-0_16
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