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The LeftRight Planarity Test
, 2009
"... A graph is planar if and only if it can be embedded in the plane without crossings. I give a detailed exposition of simple and efficient, yet poorly known algorithms for planarity testing, embedding, and Kuratowski subgraph extraction based on the leftright characterization of planarity. ..."
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A graph is planar if and only if it can be embedded in the plane without crossings. I give a detailed exposition of simple and efficient, yet poorly known algorithms for planarity testing, embedding, and Kuratowski subgraph extraction based on the leftright characterization of planarity.
Correcting and Implementing the PCtree Planarity Algorithm
"... 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 planarityrelated problems. Shih and Hsu proposed a lineartime algorithm based on a data st ..."
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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 planarityrelated problems. Shih and Hsu proposed a lineartime algorithm based on a data structure they named PCtree, which is similar to but much simpler than a PQtree. However, their presentation does not explain in detail how to implement the routines that manipulate a PCtree, and there are some nontrivial correctness and runtime issues that were not addressed in their paper. So it is far from trivial to derive a proper lineartime implementation from their description. This paper presents additions to the theoretical framework of the PCtree algorithm that are necessary to achieve correctness and linear running time. A lineartime implementation that addresses the issues raised in this paper was developed in the LEDA platform and is available.
Simplified O(n) Planarity Algorithms
, 2001
"... 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. Due to the wealth of interest from the computer science community, there are a number of remarkable but complex O(n) planar embedding algorithms. This pape ..."
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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. Due to the wealth of interest from the computer science community, there are a number of remarkable but complex O(n) planar embedding algorithms. This paper presents an O(n) planar embedding algorithm that avoids a number of the complexities of prior approaches (an early version of this work was presented at the January 1999 Symposium on Discrete Algorithms). In July 1999