An SPQR-Tree-Like Embedding Representation for Upward Planarity
arXiv:1908.00352
The paper introduces the UP-tree, a data structure that compactly represents all upward planar embeddings of biconnected single‑source directed graphs, and uses it to solve the upward planar embedding extension problem.
Abstract
The SPQR-tree is a data structure that compactly represents all planar embeddings of a biconnected planar graph. It plays a key role in constrained planarity testing. We develop a similar data structure, called the UP-tree, that compactly represents all upward planar embeddings of a biconnected single-source directed graph. We demonstrate the usefulness of the UP-tree by solving the upward planar embedding extension problem for biconnected single-source directed graphs.
Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019)