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36
An algorithm for drawing general undirected graphs
 Information Processing Letters
, 1989
"... Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets, and entit ..."
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Cited by 456 (2 self)
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Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, dataflow graphs, Petri nets, and entityrelationship diagrams, basic graph drawing algorithms are required.
An open graph visualization system and its applications to software engineering
 SOFTWARE  PRACTICE AND EXPERIENCE
, 2000
"... We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout alg ..."
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Cited by 309 (9 self)
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We describe a package of practical tools and libraries for manipulating graphs and their drawings. Our design, which aimed at facilitating the combination of the package components with other tools, includes stream and event interfaces for graph operations, highquality static and dynamic layout algorithms, and the ability to handle sizable graphs. We conclude with a description of the applications of this package to a variety of software engineering tools.
A Technique for Drawing Directed Graphs
 IEEE Transactions on Software Engineering
, 1993
"... We describe a fourpass algorithm for drawing directed graphs. The first pass finds an optimal rank assignment using a network simplex algorithm. The second pass sets the vertex order within ranks by an iterative heuristic incorporating a novel weight function and local transpositions to reduce cros ..."
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Cited by 222 (19 self)
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We describe a fourpass algorithm for drawing directed graphs. The first pass finds an optimal rank assignment using a network simplex algorithm. The second pass sets the vertex order within ranks by an iterative heuristic incorporating a novel weight function and local transpositions to reduce crossings. The third pass finds optimal coordinates for nodes by constructing and ranking an auxiliary graph. The fourth pass makes splines to draw edges. The algorithm makes good drawings and runs fast. 1.
2Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms
, 1997
"... We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NPhard, and that for the general probl ..."
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Cited by 67 (7 self)
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We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima. Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NPhard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing their results to optimum solutions.
Graph Layout through the VCG Tool
, 1994
"... The VCG tool allows the visualization of graphs that occur typically as data structures in programs. We describe the functionality of the VCG tool, its layout algorithm and its heuristics. Our main emphasis in the selection of methods is to achieve a very good performance for the layout of large gra ..."
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Cited by 52 (0 self)
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The VCG tool allows the visualization of graphs that occur typically as data structures in programs. We describe the functionality of the VCG tool, its layout algorithm and its heuristics. Our main emphasis in the selection of methods is to achieve a very good performance for the layout of large graphs. The tool supports the partitioning of edges and nodes into edge classes and nested subgraphs, the folding of regions, and the management of priorities of edges. The algorithm produces good drawings and runs reasonably fast even on very large graphs.
Synthesis of Wiring SignatureInvariant Equivalence Class Circuit Mutants and Applications to Benchmarking
, 1998
"... This paper formalizes the synthesis process of wiring signatur einvariant (WSI) combinational circuit mutants. The signature 0 is defined by a reference circuit 0, which itself is modeled as a canonic alform of a directed bipartite graph. A wiring perturbation induces a perturbed reference circuit ..."
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Cited by 28 (16 self)
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This paper formalizes the synthesis process of wiring signatur einvariant (WSI) combinational circuit mutants. The signature 0 is defined by a reference circuit 0, which itself is modeled as a canonic alform of a directed bipartite graph. A wiring perturbation induces a perturbed reference circuit. A number of mutant circuits i can be resynthesized from the perturbed circuit. The mutants of interest are the ones that belong to the wiringsignature invariant equivalenc e classN 0, i.e. the mutants i 2N 0. Cir cuit mutants i 2N 0have a number of useful properties. For any wiring perturbation, the size of the wiring signatureinvariant equivalence class is huge. Notably, circuits in this class are not random, although for un biased testing and benchmarking purp oses, mutant selections from this class are typically random. For each reference circuit, we synthesized eight equivalence subclasses of circuit mutants, based on 0 to 100 % perturbation. Each subclass contains 100 randomly chosen mutant circuits, each listed in a different random order. The 14,400 benchmarking experiments with 3200 mutants in 4 equivalence classes, covering 13 typical EDA algorithms, demonstrate that an unbiased random selection of such circuits can lead to statistically meaningful differentiation and improvements of existing and new algorithms.
An Alternative Method to Crossing Minimization on Hierarchical Graphs
 SIAM J. Optimization
, 1997
"... . A common method for drawing directed graphs is, as a first step, to partition the vertices into a set of k levels and then, as a second step, to permute the vertices within the levels such that the number of crossings is minimized. We suggest an alternative method for the second step, namely, remo ..."
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Cited by 28 (0 self)
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. A common method for drawing directed graphs is, as a first step, to partition the vertices into a set of k levels and then, as a second step, to permute the vertices within the levels such that the number of crossings is minimized. We suggest an alternative method for the second step, namely, removing the minimal number of edges such that the resulting graph is klevel planar. For the final diagram the removed edges are reinserted into a klevel planar drawing. Hence, instead of considering the klevel crossing minimization problem, we suggest solving the klevel planarization problem. In this paper we address the case k = 2. First, we give a motivation for our approach. Then, we address the problem of extracting a 2level planar subgraph of maximum weight in a given 2level graph. This problem is NPhard. Based on a characterization of 2level planar graphs, we give an integer linear programming formulation for the 2level planarization problem. Moreover, we define and investigate t...
On the Parameterized Complexity of Layered Graph Drawing
 PROC. 5TH ANNUAL EUROPEAN SYMP. ON ALGORITHMS (ESA '01
, 2001
"... We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight linesegments between vertices on adjacent layers. We prove that graphs admitting crossingfree hlayer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for ..."
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Cited by 21 (9 self)
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We consider graph drawings in which vertices are assigned to layers and edges are drawn as straight linesegments between vertices on adjacent layers. We prove that graphs admitting crossingfree hlayer drawings (for fixed h) have bounded pathwidth. We then use a path decomposition as the basis for a lineartime algorithm to decide if a graph has a crossingfree hlayer drawing (for fixed h). This algorithm is extended to solve a large number of related problems, including allowing at most k crossings, or removing at most r edges to leave a crossingfree drawing (for fixed k or r). If the number of crossings or deleted edges is a nonfixed parameter then these problems are NPcomplete. For each setting, we can also permit downward drawings of directed graphs and drawings in which edges may span multiple layers, in which case the total span or the maximum span of edges can be minimized. In contrast to the socalled Sugiyama method for layered graph drawing, our algorithms do not assume a preassignment of the vertices to layers.
A Polyhedral Approach to the MultiLayer Crossing Minimization Problem
 PROCEEDINGS OF THE INTERNATIONAL SYMPOSIUM ON GRAPH DRAWING, LECTURE NOTES IN COMPUTER SCIENCE 1353
, 1997
"... We study the multilayer crossing minimization problem from a polyhedral point of view. After the introduction of an integer programming formulation of the multilayer crossing minimization problem, we examine the 2layer case and derive several classes of facets of the associated polytope. Prelimin ..."
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Cited by 20 (2 self)
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We study the multilayer crossing minimization problem from a polyhedral point of view. After the introduction of an integer programming formulation of the multilayer crossing minimization problem, we examine the 2layer case and derive several classes of facets of the associated polytope. Preliminary computational results for 2 and 3layer instances indicate, that the usage of the corresponding facetdefining inequalities in a branchandcut approach may only lead to a practically useful algorithm, if deeper polyhedral studies are conducted.