Orderly Spanning Trees with Applications
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 , consisting of a plane graph of , and an orderly spanning tree of . 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 , and (3) the best known encodings of with O(1)-time query support. All algorithms in this paper run in linear time.
Cite
@article{arxiv.cs/0102006,
title = {Orderly Spanning Trees with Applications},
author = {Yi-Ting Chiang and Ching-Chi Lin and Hsueh-I Lu},
journal= {arXiv preprint arXiv:cs/0102006},
year = {2015}
}
Comments
25 pages, 7 figures, A preliminary version appeared in Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001), Washington D.C., USA, January 7-9, 2001, pp. 506-515