A parameterized algorithm for upward planarity testing

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 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) = kl8k and g(k,ℓ) = 23.2ℓk3.2ℓkl8k. 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. © Springer-Verlag 2004.