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- W3088572787 abstract "In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing $Gamma_H$ of a subgraph $H$ of a directed graph $G$ and asks whether $Gamma_H$ can be extended to an upward planar drawing of $G$. Our study fits into the line of research on the extensibility of partial representations, which has recently become a mainstream in Graph Drawing. We show the following results. First, we prove that the Upward Planarity Extension problem is NP-complete, even if $G$ has a prescribed upward embedding, the vertex set of $H$ coincides with the one of $G$, and $H$ contains no edge. Second, we show that the Upward Planarity Extension problem can be solved in $O(n log n)$ time if $G$ is an $n$-vertex upward planar $st$-graph. This result improves upon a known $O(n^2)$-time algorithm, which however applies to all $n$-vertex single-source upward planar graphs. Finally, we show how to solve in polynomial time a surprisingly difficult version of the Upward Planarity Extension problem, in which $G$ is a directed path or cycle with a prescribed upward embedding, $H$ contains no edges, and no two vertices share the same $y$-coordinate in $Gamma_H$." @default.
- W3088572787 created "2020-10-01" @default.
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- W3088572787 date "2019-02-18" @default.
- W3088572787 modified "2023-09-26" @default.
- W3088572787 title "Extending Upward Planar Graph Drawings" @default.
- W3088572787 doi "https://doi.org/10.48550/arxiv.1902.06575" @default.
- W3088572787 hasPublicationYear "2019" @default.
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