Book Embeddability of Series–Parallel Digraphs
Algorithmica
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Crossing-Free Acyclic Hamiltonian Path Completion for Planar st-Digraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Computing upward topological book embeddings of upward planar digraphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Crossing-Free Acyclic Hamiltonian Path Completion for Planar st-Digraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path completion (for short, HP-completion) set for embedded upward planar digraphs. In the context of book embeddings, this question becomes: given an embedded upward planar digraph G, determine whether there exists an upward 2-page book embedding of G preserving the given planar embedding.Given an embedded st-digraph G which has a crossing-free HP-completion set, we show that there always exists a crossing-free HP-completion set with at most two edges per face of G. For an embedded N-free upward planar digraph G, we show that there always exists a crossing-free acyclic HP-completion set for G which, moreover, can be computed in linear time. For a width-k embedded planar st-digraph G, we show that it can be efficiently tested whether G admits a crossing-free acyclic HP-completion set.