Correcting and Implementing the PC-tree Planarity Algorithm
BibTeX
@MISC{Boyer_correctingand,
author = {John M. Boyer and Cristina G. Fernandes and Alexandre Noma and Jose Coelho de Pina Jr.},
title = {Correcting and Implementing the PC-tree Planarity Algorithm},
year = {}
}
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Abstract
A graph is planar if it can be drawn on the plane with vertices at unique locations and no edge intersections except at the vertex endpoints. Recent research eorts have produced new algorithms for solving planarity-related problems. Shih and Hsu proposed a linear-time algorithm based on a data structure they named PC-tree, which is similar to but much simpler than a PQ-tree. However, their presentation does not explain in detail how to implement the routines that manipulate a PC-tree, and there are some nontrivial correctness and run-time issues that were not addressed in their paper. So it is far from trivial to derive a proper linear-time implementation from their description. This paper presents additions to the theoretical framework of the PC-tree algorithm that are necessary to achieve correctness and linear running time. A linear-time implementation that addresses the issues raised in this paper was developed in the LEDA platform and is available.
