Orderly Spanning Trees with Applications
Yi-Ting Chiang, Ching-Chi Lin, Hsueh-I Lu
Abstract
We introduce and study the orderly spanning trees of plane graphs. This algorithmic tool generalizes 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 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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