Results 1  10
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222
Drawing Graphs Nicely Using Simulated Annealing
, 1996
"... The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general graphs with straighline edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of ..."
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Cited by 191 (11 self)
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The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general graphs with straighline edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the "spring method" and its variants.
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 69 (6 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 55 (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.
Which crossing number is it, anyway
 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
, 1998
"... A drawing of a graph G is a mapping which assigns to each vertex a point of the plane and to each edge a simple continuous arc connecting the corresponding two points. The crossing number of G is the minimum number of crossing points in any drawing of G. We define two new parameters, as follows. The ..."
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Cited by 43 (8 self)
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A drawing of a graph G is a mapping which assigns to each vertex a point of the plane and to each edge a simple continuous arc connecting the corresponding two points. The crossing number of G is the minimum number of crossing points in any drawing of G. We define two new parameters, as follows. The pairwise crossing number (resp. the oddcrossing number) of G is the minimum number of pairs of edges that cross (resp. cross an odd number of times) over all drawings of G. We prove that the largest of these numbers (the crossing number) cannot exceed twice the square of the smallest (the oddcrossing number). Our proof is based on the following generalization of an old result of Hanani, which is of independent interest. Let G be a graph and let E0 be a subset of its edges such that there is a drawing of G, in which every edge belonging to E0 crosses any other edge an even number of times. Then G can be redrawn so that the elements of E0 are not involved in any crossing. Finally, we show that the determination of each of these parameters is an NPhard problem and it is NPcomplete in the case of the crossing number and the oddcrossing number. 1
On Linear Layouts of Graphs
, 2004
"... In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp... ..."
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Cited by 32 (20 self)
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In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A kstack (resp...
Confluent drawings: Visualizing NonPlanar Diagrams in a Planar Way
 GRAPH DRAWING (PROC. GD ’03), VOLUME 2912 OF LECTURE NOTES COMPUT. SCI
, 2003
"... We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing nonplanar graphs in a planar way. This approach allows us to draw, in a crossingfree manner, graphs—such as software interaction diagrams—that would normally have many cro ..."
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Cited by 30 (8 self)
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We introduce a new approach for drawing diagrams. Our approach is to use a technique we call confluent drawing for visualizing nonplanar graphs in a planar way. This approach allows us to draw, in a crossingfree manner, graphs—such as software interaction diagrams—that would normally have many crossings. The main idea of this approach is quite simple: we allow groups of edges to be merged together and drawn as “tracks” (similar to train tracks). Producing such confluent drawings automatically from a graph with many crossings is quite challenging, however, we offer a heuristic algorithm (one version for undirected graphs and one version for directed ones) to test if a nonplanar graph can be drawn efficiently in a confluent way. In addition, we identify several large classes of graphs that can be completely categorized as being either confluently drawable or confluently nondrawable.
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.
On the Maximum Number of
 Certain Subgraphs in KrFree Graphs, Graphs and Combinatorics 7
, 1991
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Recognizing string graphs in NP
 J. of Computer and System Sciences
"... A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable u ..."
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Cited by 25 (4 self)
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A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable until very recently, when two independent papers established exponential upper bounds on the number of intersections needed to realize a string graph (Pach and Tóth, 2001; Schaefer and ˇ Stefankovič, 2001). These results implied that the recognition problem lies in NEXP. In the present paper we improve this by showing that the recognition problem for string graphs is in NP, and therefore NPcomplete, since Kratochvíl showed that the recognition problem is NPhard (Kratochvíl, 1991b). The result has consequences for the computational complexity of problems in graph drawing, and topological inference. We also show that the string graph problem is decidable for surfaces of arbitrary genus. Key words: String graphs, NPcompleteness, graph drawing, topological inference, Euler diagrams