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A TopologyShapeMetrics Approach for the Automatic Layout of UML Class Diagrams
"... Class diagrams are among the most popular visualizations for object oriented software systems and have a broad range of applications. In many settings it is desirable that the placement of the diagram elements is determined automatically, especially when the diagrams are generated automatically whic ..."
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Cited by 16 (0 self)
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Class diagrams are among the most popular visualizations for object oriented software systems and have a broad range of applications. In many settings it is desirable that the placement of the diagram elements is determined automatically, especially when the diagrams are generated automatically which is usually the case in reverse engineering. For this reason the automatic layout of class diagram gained importance in the last years. Current approaches for the automatic layout of class diagrams are based on the hierarchic graph drawing paradigm. These algorithms produce good results for class diagrams with large and deep structural information, i.e., diagrams with a large and deep inheritance hierarchy. However, they do not perform satisfactorily in absence of this information. We propose in this work a new algorithm for automatic layout of class diagram which is based on the topologyshapemetrics approach. The algorithm is an adaption of sophisticated graph drawing algorithms which have proven their effectiveness in many applications. The algorithm works as well for class diagrams with rich structural information as for class diagrams with few or no structural information. It improves therefore the existing algorithms significantly. An implementation of the algorithm is used in the reverse engineering tool JarInspector.
Layerfree upward crossing minimization
 ACM Journal of Experimental Algorithmics
"... Abstract. An upward drawing of a DAG G is a drawing of G in which all edges are drawn as curves increasing monotonically in the vertical direction. In this paper, we present a new approach for upward crossing minimization, i.e., finding an upward drawing of a DAG G with as few crossings as possible. ..."
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Abstract. An upward drawing of a DAG G is a drawing of G in which all edges are drawn as curves increasing monotonically in the vertical direction. In this paper, we present a new approach for upward crossing minimization, i.e., finding an upward drawing of a DAG G with as few crossings as possible. Our algorithm is based on a twostage upward planarization approach, which computes a feasible upward planar subgraph in the first step, and reinserts the remaining edges by computing constraintfeasible upward insertion paths. An experimental study shows that the new algorithm leads to much better results than existing algorithms for upward crossing minimization, including the classical Sugiyama approach. 1
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 13 (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.
An SDP Approach to Multilevel Crossing Minimization
"... We present an approach based on semidefinite programs (SDP) to tackle the multilevel crossing minimization problem. Thereby, we are given a layered graph (i.e., the graph’s vertices are assigned to multiple parallel levels) and ask for an ordering of the nodes on their levels such that, when drawin ..."
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Cited by 7 (5 self)
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We present an approach based on semidefinite programs (SDP) to tackle the multilevel crossing minimization problem. Thereby, we are given a layered graph (i.e., the graph’s vertices are assigned to multiple parallel levels) and ask for an ordering of the nodes on their levels such that, when drawing the graph with straight lines, the resulting number of crossings is minimized. Solving this step is crucial in the probably most widely used graph drawing scheme, the socalled Sugiyama framework. The problem has received a lot of attention both in the field of heuristics and exact methods. For a long time, integer linear programming (ILP) approaches were the only exact algorithms applicable at least to small graphs. Recently, SDP formulations for the special case of two levels were proposed
Upward Planarization Layout
, 2011
"... Recently, we presented a new practical method for upward crossing minimization [8], which clearly outperformed existing approaches for drawing hierarchical graphs in that respect. The outcome of this method is an upward planar representation (UPR), a planarly embedded graph in which crossings are re ..."
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Cited by 7 (3 self)
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Recently, we presented a new practical method for upward crossing minimization [8], which clearly outperformed existing approaches for drawing hierarchical graphs in that respect. The outcome of this method is an upward planar representation (UPR), a planarly embedded graph in which crossings are represented by dummy vertices. However, straightforward approaches for drawing such UPRs lead to quite unsatisfactory results. In this paper, we present a new algorithm for drawing UPRs that greatly improves the layout quality, leading to good hierarchal drawings with few crossings. We analyze its performance on wellknown benchmark graphs and compare it with alternative approaches.
Global kLevel Crossing Reduction
, 2011
"... Directed graphs are commonly drawn by a four phase framework introduced by Sugiyama et al. in 1981. The vertices are placed on parallel horizontal levels. The edge routing between consecutive levels is computed by solving onesided 2level crossing minimization problems, which are repeated in up and ..."
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Cited by 4 (2 self)
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Directed graphs are commonly drawn by a four phase framework introduced by Sugiyama et al. in 1981. The vertices are placed on parallel horizontal levels. The edge routing between consecutive levels is computed by solving onesided 2level crossing minimization problems, which are repeated in up and down sweeps over all levels. Crossing minimization problems are generally N Phard. We introduce a global crossing reduction, which at any particular time considers all crossings between all levels. Our approach is based on the sifting technique. It yields an improvement of 5 – 10 % in the number of crossings over the levelbylevel onesided 2level crossing reduction heuristics. In addition, it avoids type 2 conflicts which are crossings between edges whose endpoints are dummy vertices. This helps straightening long edges spanning many levels. Finally, the global crossing reduction approach can directly be extended to cyclic, radial, and clustered level graphs achieving similar improvements. The running time is quadratic in the size of the input graph, whereas the common levelbylevel approaches are faster but operate on larger graphs with many dummy vertices for long edges. Submitted:
Efficient Management of Transcoding and Multicasting Multimedia Streams
"... Management of multimedia applications is a very challenging task. This is especially true in the emerging new Internet where users use devices such as smart phones and PDAs, a considerable amount of them are connected via wireless connections, and peer to peer applications are becoming more and more ..."
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Cited by 2 (0 self)
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Management of multimedia applications is a very challenging task. This is especially true in the emerging new Internet where users use devices such as smart phones and PDAs, a considerable amount of them are connected via wireless connections, and peer to peer applications are becoming more and more popular. In this new environment, the multimedia format that should be sent to different users varies considerably and sending a media stream to a set of users often involves transcoding of formats. This paper addresses the problem of managing multicast streaming in this new environment by defining a framework in which transcoding can be done in internal network nodes, and not necessarily at the sender’s or at the receivers ’ ends. In this framework the sender retrieves all information regarding the transcoding abilities of the various nodes and the characteristics of the links. Then, it needs to decide how to broadcast the multimedia stream, in what formats, and where to perform the needed transcoding. We show that this algorithmic problem is NPhard (and also hard to approximate). However, for the very practical case where the number of relevant formats is small, we present an efficient approximation scheme. We study, using simulations, the actual performance of our algorithm and compare it to transcoding at the sender’s or at the receivers ’ ends. Our results indicate that performing transcoding in intermediate nodes is indeed efficient, and that our algorithm can find a much better streaming scheme than any known algorithm. 1
Upward Planarity Testing via SAT
"... Abstract. A directed acyclic graph is upward planar if it allows a drawing without edge crossings where all edges are drawn as curves with monotonously increasing ycoordinates. The problem to decide whether a graph is upward planar or not is NPcomplete in general, and while special graph classes a ..."
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Cited by 1 (1 self)
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Abstract. A directed acyclic graph is upward planar if it allows a drawing without edge crossings where all edges are drawn as curves with monotonously increasing ycoordinates. The problem to decide whether a graph is upward planar or not is NPcomplete in general, and while special graph classes are polynomial time solvable, there is not much known about solving the problem for general graphs in practice. The only attempt so far was a branchandbound algorithm over the graph’s triconnectivity structure which was able to solve sparse graphs. In this paper, we propose a fundamentally different approach, based on the seemingly novel concept of ordered embeddings. We carefully model the problem as a special SAT instance, i.e., a logic formula for which we check satisfiability. Solving these SAT instances allows us to decide upward planarity for arbitrary graphs. We then show experimentally that this approach seems to dominate the known alternative approaches and is able to solve traditionally used graph drawing benchmarks effectively. 1
Multilevel verticality optimization: Concept, strategies, and drawing scheme
, 2011
"... Abstract. In traditional multilevel graph drawing—known as Sugiyama’s framework—the number of crossings is considered one of the most important goals. Herein, we propose the alternative concept of optimizing the verticality of the drawn edges. We formally specify the problem, discuss its relative m ..."
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Cited by 1 (1 self)
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Abstract. In traditional multilevel graph drawing—known as Sugiyama’s framework—the number of crossings is considered one of the most important goals. Herein, we propose the alternative concept of optimizing the verticality of the drawn edges. We formally specify the problem, discuss its relative merits, and show that drawings that are good w.r.t. verticality in fact also have a low number of crossings. We present heuristic and exact approaches to tackle the verticality problem and study them in practice. Furthermore, we present a new drawing scheme (inherently bundling edges and drawing them monotonously), especially suitable for verticality optimization. It works without the traditional subdivision of edges, i.e., edges may span multiple levels, and therefore potentially allows to tackle larger graphs. 1