Crossing-Optimal Acyclic HP-Completion for Outerplanar st-Digraphs

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:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

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Abstract

Given an embedded planar acyclic digraph G , the acyclic hamiltonian path completion with crossing minimization (Acyclic- HPCCM) problem is to determine 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 a hamiltonian acyclic digraph. In this paper, we present a linear time algorithm which solves the Acyclic-HPCCM problem on any outerplanar st -digraph G . The algorithm is based on properties of the optimal solution and an st-polygon decomposition of G . As a consequence of our result, we can obtain for the class of outerplanar st -digraphs upward topological 2-page book embeddings with minimum number of spine crossings.