# Upward drawings of acyclic digraphs

Layout Of Graphs

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## Abstract

The problem of representing acyclic digraphs in the plane is considered. We present algorithms that construct planar drawings of acyclic digraphs such that all edges are straight-line segments flowing in the same direction, e.g., from the left to the right or from the bottom to the top. The time complexity for constructing such *upward drawings* is *O* (*n* log *n*), where *n* is the number of vertices of the digraph. For covering digraphs of lattices (Hasse diagrams), the complexity is reduced to *O*(*n*). We also show that the planar digraphs that admit an upward drawing are exactly the subgraphs of planar *st-graphs*.

## Keywords

Planar Graph Candidate List Dual Graph Plane Representation Hasse Diagram
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© Springer-Verlag Berlin Heidelberg 1988