A Parameterized Algorithm for Upward Planarity Testing

(Extended Abstract)
  • Hubert Chan
Conference paper

DOI: 10.1007/978-3-540-30140-0_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3221)
Cite this paper as:
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

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)n3 + 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hubert Chan
    • 1
  1. 1.School of Computer ScienceUniversity of WaterlooCanada

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