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arXiv · cs/0102006

Orderly Spanning Trees with Applications

Yi-Ting Chiang·Ching-Chi Lin·Hsueh-I Lu
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Abstract

We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an {\em orderly pair} for any connected planar graph $G$, consisting of a plane graph $H$ of $G$, and an orderly spanning tree of $H$. We also present several applications of orderly spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem, (2) the first area-optimal 2-visibility drawing of $G$, and (3) the best known encodings of $G$ with O(1)-time query support. All algorithms in this paper run in linear time.

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Yi-Ting Chiang, Ching-Chi Lin, Hsueh-I Lu. 2001-02-07. Orderly Spanning Trees with Applications. https://doi.org/10.1137/s0097539702411381

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