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16
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 520 (40 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
Upward Planarity Testing
 SIAM Journal on Computing
, 1995
"... Acyclic digraphs, such as the covering digraphs of ordered sets, are usually drawn upward, i.e., with the edges monotonically increasing in the vertical direction. A digraph is upward planar if it admits an upward planar drawing. In this survey paper, we overview the literature on the problem of upw ..."
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Cited by 81 (15 self)
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Acyclic digraphs, such as the covering digraphs of ordered sets, are usually drawn upward, i.e., with the edges monotonically increasing in the vertical direction. A digraph is upward planar if it admits an upward planar drawing. In this survey paper, we overview the literature on the problem of upward planarity testing. We present several characterizations of upward planarity and describe upward planarity testing algorithms for special classes of digraphs, such as embedded digraphs and singlesource digraphs. We also sketch the proof of NPcompleteness of upward planarity testing.
Optimal upward planarity testing of singlesource digraphs
 SIAM Journal on Computing
, 1998
"... Abstract. A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in softwar ..."
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Cited by 34 (4 self)
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Abstract. A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of singlesource digraphs; we provide a new combinatorial characterization of upward planarity and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a singlesource digraph with n vertices is upward planar in O(n) sequential time, and in O(log n) time on a CRCW PRAM with n log log n / log n processors, using O(n) space. The algorithm also constructs an upward planar drawing if the test is successful. The previously known best result is an O(n2)time algorithm by Hutton and Lubiw [Proc. 2nd ACM–SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1991, pp. 203–211]. No efficient parallel algorithms for upward planarity testing were previously known.
Planar Drawings and Angular Resolution: Algorithms and Bounds (Extended Abstract)
 IN PROC. 2ND ANNU. EUROPEAN SYMPOS. ALGORITHMS
, 1994
"... We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straightline drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on th ..."
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Cited by 24 (5 self)
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We investigate the problem of constructing planar straightline drawings of graphs with large angles between the edges. Namely, we study the angular resolution of planar straightline drawings, defined as the smallest angle formed by two incident edges. We prove the first nontrivial upper bound on the angular resolution of planar straightline drawings, and show a continuous tradeoff between the area and the angular resolution. We also give lineartime algorithms for constructing planar straightline drawings with high angular resolution for various classes of graphs, such as seriesparallel graphs, outerplanar graphs, and triangulations generated by nested triangles. Our results are obtained by new techniques that make extensive use of geometric constructions.
Constraints in graph drawing algorithms
 Constraints
, 1998
"... Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and g ..."
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Cited by 15 (0 self)
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Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and graphical user interfaces. In this paper, we survey algorithmic techniques for graph drawing that support the expression and satisfaction of userdefined constraints. 1.
Drawing Graphs by Example Efficiently: Trees and Planar Acyclic Digraphs (Extended Abstract)
 Graph Drawing (Proc. GD '94), volume 894 of Lecture Notes in Computer Science
, 1995
"... ) Isabel F. Cruz 1 and Ashim Garg 2 1 Department of Electrical Engineering and Computer Science Tufts University Medford, MA 02155, USA 2 Department of Computer Science Brown University Providence, RI 029121910, USA Abstract. Constraintbased graph drawing systems provide expressive power ..."
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Cited by 13 (7 self)
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) Isabel F. Cruz 1 and Ashim Garg 2 1 Department of Electrical Engineering and Computer Science Tufts University Medford, MA 02155, USA 2 Department of Computer Science Brown University Providence, RI 029121910, USA Abstract. Constraintbased graph drawing systems provide expressive power and flexibility. Previously proposed approaches make use of general constraint solvers, which are inefficient, and of textual specification of constraints, which can be long and difficult to understand. In this paper we propose the use of a constraintbased visual language for constructing planar drawings of trees, seriesparallel graphs, and acyclic digraphs in linear time. A graph drawing system based on our approach can therefore provide the power of constraintbased graph drawing, the simplicity of visual specifications, and the computational efficiency that is typical of the algorithmicbased approaches. 1 Introduction It is common practice to explain the layout of a graph using pictu...
Spirality And Optimal Orthogonal Drawings
 SIAM J. Comput
, 1998
"... . We deal with the problem of constructing the orthogonal drawing of a graph with the minimum number of bends along the edges. The problem has been recently shown to be NPcomplete in the general case. In this paper we introduce and study the new concept of spirality, which is a measure of ..."
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Cited by 13 (3 self)
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.<F3.8e+05> We deal with the problem of constructing the orthogonal drawing of a graph with the minimum number of bends along the edges. The problem has been recently shown to be NPcomplete in the general case. In this paper we introduce and study the new concept of spirality, which is a measure of how an orthogonal drawing is "rolled up," and develop a theory on the interplay between spirality and number of bends of orthogonal drawings. We exploit this theory to present polynomial time algorithms for two significant classes of graphs: seriesparallel graphs and 3planar graphs. Seriesparallel graphs arise in a variety of problems such as scheduling, electrical networks, dataflow analysis, database logic programs, and circuit layout. Also, they play a central role in planarity problems. Furthermore, drawings of 3planar graphs are a classical field of investigation.<F4.005e+05> Key words.<F3.8e+05> graph drawing, orthogonal representation, planar embedding, bend minimization<F4.005e+...
Drawing Directed Acyclic Graphs: An Experimental Study
, 1996
"... In this paper we consider the class of directed acyclic graphs (DAGs), and present the results of an experimental study on four drawing algorithms specifically developed for DAGs. Our study is conducted on two large test suites of DAGs and yields more than 30 charts comparing the performance of ..."
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Cited by 11 (0 self)
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In this paper we consider the class of directed acyclic graphs (DAGs), and present the results of an experimental study on four drawing algorithms specifically developed for DAGs. Our study is conducted on two large test suites of DAGs and yields more than 30 charts comparing the performance of the drawing algorithms with respect to several quality measures, including area, crossings, bends, and aspect ratio. The algorithms exhibit various tradeoffs with respect to the quality measures, and none of them clearly outperforms the others.
Computing Orthogonal Drawings in a Variable Embedding Setting
 In [57
, 1998
"... This paper addresses the classical graph drawing problem of designing an algorithm that computes an orthogonal representation with the minimum number of bends. The algorithm receives as input a 4planar graph with a given ordering of the edges around the vertices and is allowed to change such orderi ..."
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Cited by 5 (1 self)
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This paper addresses the classical graph drawing problem of designing an algorithm that computes an orthogonal representation with the minimum number of bends. The algorithm receives as input a 4planar graph with a given ordering of the edges around the vertices and is allowed to change such ordering to reach the optimum. While the general problem has been shown to be NP complete [10], polynomial time algorithms have been devised for graphs whose vertex degree is at most three [5]. We show the first algorithm whose time complexity is exponential only in the number of vertices of degree four of the input graph. This settles a problem left as open in [6]. Our algorithm is further extended to handle graphs with vertices of degree higher than four. The analysis of the algorithm is supported by several experiments on the structure of a large set of input graphs. 1 Introduction and Overview Graph drawing is concerned with the design of methods for the automatic display of graphs so as to ...
Advances in the Theory and Practice of Graph Drawing
 Theor. Comp. Sci
, 1996
"... The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph d ..."
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Cited by 4 (0 self)
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The visualization of conceptual structures is a key component of support tools for complex applications in science and engineering. Foremost among the visual representations used are drawings of graphs and ordered sets. In this talk, we survey recent advances in the theory and practice of graph drawing. Specific topics include bounds and tradeoffs for drawing properties, threedimensional representations, methods for constraint satisfaction, and experimental studies. 1 Introduction In this paper, we survey selected research trends in graph drawing, and overview some recent results of the author and his collaborators. Graph drawing addresses the problem of constructing geometric representations of graphs, a key component of support tools for complex applications in science and engineering. Graph drawing is a young research field that has growth very rapidly in the last decade. One of its distinctive characteristics is to have furthered collaborative efforts between computer scien...