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StraightLine Drawing Algorithms for Hierarchical Graphs and Clustered Graphs
 Algorithmica
, 1999
"... Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualizatio ..."
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Cited by 59 (12 self)
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Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in CASE tools, software visualization, and VLSI design. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of straightline representation has not been solved completely. In this paper, we answer the question: does every planar hierarchical graph admit a planar straightline hierarchical drawing? We present an algorithm that constructs such drawings in linear time. Also, we answer a basic question for clustered graphs, that is, does every planar clustered graph admit a planar straightline drawing with clusters drawn as convex polygons? We provide a method for such drawings based on our algorithm for hierarchical graphs.
On the cutting edge: Simplified O(n) planarity by edge addition
 Journal of Graph Algorithms and Applications
, 2004
"... www.cs.uvic.ca/˜wendym ..."
Characterization of unlabeled level planar trees
 14TH SYMPOSIUM ON GRAPH DRAWING (GD), VOLUME 4372 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j)  x ∈ R}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an nlevel gr ..."
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Cited by 13 (7 self)
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Consider a graph G drawn in the plane so that each vertex lies on a distinct horizontal line ℓj = {(x, j)  x ∈ R}. The bijection φ that maps the set of n vertices V to a set of distinct horizontal lines ℓj forms a labeling of the vertices. Such a graph G with the labeling φ is called an nlevel graph and is said to be nlevel planar if it can be drawn with straightline edges and no crossings while keeping each vertex on its own level. In this paper, we consider the class of trees that are nlevel planar regardless of their labeling. We call such trees unlabeled level planar (ULP). Our contributions are threefold. First, we provide a complete characterization of ULP trees in terms of a pair of forbidden subtrees. Second, we show how to draw ULP trees in linear time. Third, we provide a linear time recognition algorithm for ULP trees.
Characterisation of Level NonPlanar Graphs by Minimal Patterns
 Computing and Combinatorics, 6th Annual International Conference, COCOON 2000, volume 1858 of LNCS
, 1998
"... In this paper we develop a characterisation of minimal nonplanarity of level graphs. We show that a level minimal nonplanar (LMNP) graph is completely characterised by either a tree, a level nonplanar cycle or a level planar cycle with certain path augmentations. We discuss the usefulness of thes ..."
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Cited by 4 (1 self)
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In this paper we develop a characterisation of minimal nonplanarity of level graphs. We show that a level minimal nonplanar (LMNP) graph is completely characterised by either a tree, a level nonplanar cycle or a level planar cycle with certain path augmentations. We discuss the usefulness of these characterisations in the context of an branchandcut Integer Linear Programming implementation of the Maximum Level Planar Subgraph (MLPS) problem and conjecture that the inequalities associated with level minimal nonplanar subgraphs are facetdefining for the MLPS polytope. 1 Introduction Graph layout by Integer Linear Programming (ILP) has gained remarkable success recently. The method has, generally, the following framework: ffl compute the planar subgraph having the maximum number of edges by ILP; ffl compute the layout of the planar subgraph by an exact polynomialtime algorithm; and, ffl add nonplanar edges to the layout. This approach has various advantages compared to other ...
Drawing Database Schemas
 Software  Practice and Experience
"... A wide number of practical applications would benefit from automatically generated graphical representations of database schemas, in which tables are represented by boxes, and table attributes correspond to distinct stripes inside each table. Links, connecting attributes of two different tables, rep ..."
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Cited by 2 (0 self)
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A wide number of practical applications would benefit from automatically generated graphical representations of database schemas, in which tables are represented by boxes, and table attributes correspond to distinct stripes inside each table. Links, connecting attributes of two different tables, represent referential constraints or join relationships, and may attach arbitrarily to the left or to the right side of the stripes representing the attributes. To our knowledge no drawing technique is available to automatically produce diagrams in such strongly constrained drawing convention. In this paper we provide a polynomial time algorithm for solving this problem and test its efficiency and effectiveness against a large test suite. Also, we describe an implementation of a system that uses such an algorithm and we study the main methodological problems we faced in developing such a technology.
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).
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.
Subgraph Homeomorphism via the Edge Addition Planarity Algorithm
, 2012
"... This paper extends the edge addition planarity algorithm from Boyer and Myrvold to provide a new way of solving the subgraph homeomorphism problem for K2,3, K4, and K3,3. These extensions derive much of their behavior and correctness from the edge addition planarity algorithm, providing an alternati ..."
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This paper extends the edge addition planarity algorithm from Boyer and Myrvold to provide a new way of solving the subgraph homeomorphism problem for K2,3, K4, and K3,3. These extensions derive much of their behavior and correctness from the edge addition planarity algorithm, providing an alternative perspective on these subgraph homeomorphism problems based on affinity with planarity rather than triconnectivity. Reference implementations of these algorithms have been made available in an open source project