Crossing-Optimal Acyclic Hamiltonian Path Completion and Its Application to Upward Topological Book Embeddings

  • Authors:

  • Tamara Mchedlidze;Antonios Symvonis

  • Affiliations:

  • Dept. of Mathematics, National Technical University of Athens, Athens, Greece;Dept. of Mathematics, National Technical University of Athens, Athens, Greece

  • Venue:
  • WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
  • Year:
  • 2009

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Abstract

Given an embedded planar acyclic digraph G , we define the problem of acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM) to be the problem of determining a hamiltonian path completion set of edges such that, when these edges are embedded on G , they create the smallest possible number of edge crossings and turn G to an acyclic hamiltonian digraph. Our results include: 1 We provide a characterization under which a triangulated st -digraph G is hamiltonian. 1 For the class of planar st -digraphs, we establish an equivalence between the Acyclic-HPCCM problem and the problem of determining an upward 2-page topological book embedding with minimum number of spine crossings. Based on this equivalence we infer for the class of outerplanar triangulated st -digraphs an upward topological 2-page book embedding with minimum number of spine crossings and at most one spine crossing per edge.