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On the cutting edge: Simplified O(n) planarity by edge addition
 Journal of Graph Algorithms and Applications
, 2004
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Algorithms for Drawing Clustered Graphs
, 1997
"... In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics ..."
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In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics workstation as graph drawings. The usefulness of the relational model depends on whether the graph drawings effectively convey the relational information to the users. This thesis is concerned with finding good drawings of graphs. As the amount of information that we want to visualize becomes larger and the relations become more complex, the classical graph model tends to be inadequate. Many extended models use a node hierarchy to help cope with the complexity. This thesis introduces a new graph model called the clustered graph. The central theme of the thesis is an investigation of efficient algorithms to produce good drawings for clustered graphs. Although the criteria for judging the qua...
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
COMP 122: Algorithms and Analysis Testing Graph Planarity (Part 1 of 2)
, 1996
"... Introduction In these two lectures, we will discuss the algorithm developed by Hopcroft and Tarjan [6] for efficiently testing whether a graph G = (V; E) is planar. This is an extremely elegant algorithm that runs in O(V) time, and brings together a number of algorithms and data structures that we ..."
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Introduction In these two lectures, we will discuss the algorithm developed by Hopcroft and Tarjan [6] for efficiently testing whether a graph G = (V; E) is planar. This is an extremely elegant algorithm that runs in O(V) time, and brings together a number of algorithms and data structures that we have seen previously in class: radix sort, depth first search, biconnected components, and stacks. As I mentioned on the first day of class, the graph planarity problem has practical applications, e.g., in deciding whether a given electrical circuit can be laid out on a printed circuit board. While the HopcroftTarjan algorithm is complex, it is a "classic in computational graph theory" and "a superb example of the design of an efficient graph algorithm" [1]. We are studying this algorithm precisely for this reason. I am aware of two textbooks [3, 7] that describe the algorithm. The problem of graph plan