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16
Planar Polyline Drawings with Good Angular Resolution
 Graph Drawing (Proc. GD '98), volume 1547 of LNCS
, 1998
"... . We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree d on a (2n \Gamma 5) \Theta ( 3 2 n \Gamma 7 2 ) grid with at most 5n \Gamma 15 bends and minimum angle ? 2 d . In the constructed drawings, every edge h ..."
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Cited by 22 (1 self)
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. We present a linear time algorithm that constructs a planar polyline grid drawing of any plane graph with n vertices and maximum degree d on a (2n \Gamma 5) \Theta ( 3 2 n \Gamma 7 2 ) grid with at most 5n \Gamma 15 bends and minimum angle ? 2 d . In the constructed drawings, every edge has at most three bends and length O(n). To our best knowledge, this algorithm achieves the best simultaneous bounds concerning the grid size, angular resolution, and number of bends for planar grid drawings of highdegree planar graphs. Besides the nice theoretical features, the practical drawings are aesthetically very pleasing. An implementation of our algorithm is available with the AGDLibrary (Algorithms for Graph Drawing) [2, 1]. Our algorithm is based on ideas by Kant for polyline grid drawings for triconnected plane graphs [23]. In particular, our algorithm significantly improves upon his bounds on the angular resolution and the grid size for nontriconnected plane graphs....
SketchDriven Orthogonal Graph Drawing
, 2002
"... We present an orthogonal graph drawing algorithm that uses a sketchy drawing of the graph as input. While the algorithm produces an orthogonal drawing with few bends in the Kandinsky model it also preserves the general appearance of the sketch. Potential applications for this kind of drawing alg ..."
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Cited by 18 (4 self)
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We present an orthogonal graph drawing algorithm that uses a sketchy drawing of the graph as input. While the algorithm produces an orthogonal drawing with few bends in the Kandinsky model it also preserves the general appearance of the sketch. Potential applications for this kind of drawing algorithm include the generation of schematic maps from geographic networks and interactive orthogonal graph drawing.
A New Approach for Visualizing UML Class Diagrams
"... UML diagrams have become increasingly important in the engineering and reengineering processes for software systems. Of particular interest are UML class diagrams whose purpose is to display class hierarchies (generalizations), associations, aggregations, and compositions in one picture. The combina ..."
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Cited by 14 (0 self)
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UML diagrams have become increasingly important in the engineering and reengineering processes for software systems. Of particular interest are UML class diagrams whose purpose is to display class hierarchies (generalizations), associations, aggregations, and compositions in one picture. The combination of hierarchical and nonhierarchical relations poses a special challenge to a graph layout tool. Existing layout tools treat hierarchical and nonhierarchical relations either alike or as separate tasks in a twophase process as in, e.g., [Seemann 1997]. We suggest a new approach for visualizing UML class diagrams leading to a balanced mixture of the following aesthetic criteria: Crossing minimization, bend minimization, uniform direction within each class hierarchy, no nesting of one class hierarchy within another, orthogonal layout, merging of multiple inheritance edges, and good edge labelling. We have realized our approach within the graph drawing library GoVisual. Experiments show the superiority to stateoftheart and industrial standard layouts.
Orthogonal Graph Drawing with Constraints
 In Proc. 11th ACMSIAM Symposium on Discrete Algorithms
, 2000
"... One of the primary prerequisites of drawing a graph directly from practical application is that the user must be able to formulate constraints for the layout. We introduce a concept to incorporate various kinds of constraints in the wellknown model for bendminimizing orthogonal drawings for planar ..."
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Cited by 9 (2 self)
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One of the primary prerequisites of drawing a graph directly from practical application is that the user must be able to formulate constraints for the layout. We introduce a concept to incorporate various kinds of constraints in the wellknown model for bendminimizing orthogonal drawings for planar and nonplanar graphs which was originally based on a mincostflow approach. Using ILP formulations, we drastically improve the flexibility of the basic system and enable a possibly effective user interaction while ensuring efficient algorithms. Via some examples we are able to demonstrate our realization of this concept.
An Experimental Comparison of Orthogonal Compaction Algorithms
 In Graph Drawing (Proc. GD 2000
, 2000
"... We present an experimental study in which we compare the stateoftheart methods for compacting orthogonal graph layouts. Given the shape of a planar orthogonal drawing, the task is to place the vertices and the bends on grid points so that the total area or the total edge length is minimised. We c ..."
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Cited by 7 (2 self)
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We present an experimental study in which we compare the stateoftheart methods for compacting orthogonal graph layouts. Given the shape of a planar orthogonal drawing, the task is to place the vertices and the bends on grid points so that the total area or the total edge length is minimised. We compare four constructive heuristics based on rectangular dissection and on turnregularity, also in combination with two improvement heuristics based on longest paths and network flows, and an exact method which is able to compute provable optimal drawings of minimum total edge length. We provide a performance evaluation in terms of quality and running time. The test data consists of two testsuites already used in previous experimental research. In order to get hard instances, we randomly generated an additional set of planar graphs.
Fast Compaction for Orthogonal Drawings with Vertices of Prescribed Size
 IN MUTZEL ET AL
, 2001
"... In this paper, we present a new compaction algorithm which computes orthogonal drawings where the size of the vertices is given as input. This is a critical constraint for many practical applications like UML. The algorithm provides a drastic improvement on previous approaches. It has linear worst c ..."
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Cited by 6 (1 self)
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In this paper, we present a new compaction algorithm which computes orthogonal drawings where the size of the vertices is given as input. This is a critical constraint for many practical applications like UML. The algorithm provides a drastic improvement on previous approaches. It has linear worst case running time and experiments show that it performs very well in practice.
Orthogonal Drawings Based On The Stratification Of Planar Graphs
, 2000
"... Several algorithms have been proposed to draw planar graphs using 2visibility and Kandinsky Models. Here, we propose three new algorithms implementing these models in linear time using small grid sizes and few bends. These algorithms are all based on the construction of a particular layered spannin ..."
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Cited by 4 (2 self)
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Several algorithms have been proposed to draw planar graphs using 2visibility and Kandinsky Models. Here, we propose three new algorithms implementing these models in linear time using small grid sizes and few bends. These algorithms are all based on the construction of a particular layered spanning tree called Stratification. A linear time algorithm that computes a stratification is also presented.
Graph Drawing Algorithm Engineering with AGD
, 2000
"... We discuss the algorithm engineering aspects of AGD, a software library of algorithms for graph drawing. AGD represents algorithms as classes that provide one or more methods for calling the algorithm. There is a common base class, also called the type of an algorithm, for algorithms providing basic ..."
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Cited by 3 (2 self)
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We discuss the algorithm engineering aspects of AGD, a software library of algorithms for graph drawing. AGD represents algorithms as classes that provide one or more methods for calling the algorithm. There is a common base class, also called the type of an algorithm, for algorithms providing basically the same functionality. This enables us to exchange components and experiment with various algorithms and implementations of the same type. We give examples for algorithm engineering with AGD for drawing general nonhierarchical graphs and hierarchical graphs.
Accelerated bend minimization
, 2012
"... We present an O(n 3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n 7/4 √ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, ..."
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Cited by 2 (1 self)
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We present an O(n 3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n 7/4 √ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated mincost flow problem on a planar bidirected graph with bounded costs and face sizes in O(n 3/2) time.