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Orderly Spanning Trees with Applications | | Yi-Ting Chiang
; Ching-Chi Lin
; Hsueh-I Lu
; | | Date: |
7 Feb 2001 | | Subject: | Data Structures and Algorithms; Discrete Mathematics ACM-class: F.2.2; G.2.2; E.4; E.1 | cs.DS cs.DM | | 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. | | Source: | arXiv, cs.DS/0102006 | | Services: | Forum | Review | PDF | Favorites | |
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