Upward Point Set Embeddability for Convex Point Sets Is in P
In this paper, we present a polynomial dynamic programming algorithm that tests whether a n-vertex directed tree T has an upward planar embedding into a convex point-set S of size n. We also note that our approach can be extended to the class of outerplanar digraphs. This nontrivial and surprising result implies that any given digraph can be efficiently tested for an upward planar embedding into a given convex point set.
KeywordsPlanar Graph Directed Tree Dynamic Programming Algorithm Consecutive Point Outerplanar Graph
- 15.Kaufmann, M., Mchedlidze, T., Symvonis, A.: Upward point set embeddability for convex point sets is in P. Technical report. arXiv:1108.3092, http://arxiv.org/abs/1108.3092