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65
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 ..."
Abstract

Cited by 515 (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.
Automatic graph drawing and readability of diagrams
 IEEE Transactions on Systems, Man and Cybernetics
, 1988
"... AhtractDiagrams are widely used in several areas of computer wience, and their effectiveness is thoroughly recognized. One of the main qualities requested for them is readability; this is especially, but not exclusively, true in the area of information systems, where diagrams are used to model data ..."
Abstract

Cited by 91 (8 self)
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AhtractDiagrams are widely used in several areas of computer wience, and their effectiveness is thoroughly recognized. One of the main qualities requested for them is readability; this is especially, but not exclusively, true in the area of information systems, where diagrams are used to model data and functions of the application. Up to now, diagrams have been produced manually or with the aid of a graphic editor; in both caws placement of symbols and routing of connections are under responsibility of the designer. The goal of the work is to investigate how readability of diagrams can be achieved by means of automatic tools. Existing results in the literature are compared, and a comprehensive algorithmic approach to the problem is proposed. The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures. Finally, several applications of a graphic tool that embodies the aforementioned facility are shown. I.
A Lineartime Algorithm for Drawing a Planar Graph on a Grid
 Information Processing Letters
, 1989
"... We present a lineartime algorithm that, given an nvertex planar graph G, finds an embedding of G into a (2n \Gamma 4) \Theta (n \Gamma 2) grid such that the edges of G are straightline segments. 1 Introduction We consider the problem of embedding the vertices of a planar graph into a small grid i ..."
Abstract

Cited by 36 (5 self)
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We present a lineartime algorithm that, given an nvertex planar graph G, finds an embedding of G into a (2n \Gamma 4) \Theta (n \Gamma 2) grid such that the edges of G are straightline segments. 1 Introduction We consider the problem of embedding the vertices of a planar graph into a small grid in the plane in such a way that the edges are straight, nonintersecting line segments. The existence of such straightline embeddings for planar graphs was independently discovered by F'ary [Fa48], Stein [St51], and Wagner [Wa36]; this result also follows from Steinitz's theorem on convex polytopes in three dimensions [SR34]. The first algorithms for constructing straightline embeddings [Tu63, CYN84, CON85] required highprecision arithmetic, and the resulting drawings were not very aesthetic, since they tend to produce uneven distributions of vertices over the drawing area. Rosenstiehl and Tarjan [RT86] noticed that it would be convenient to be able to map veritices of a planar graph into a...
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.
On Rectangle Visibility Graphs
, 1997
"... We study the problem of drawing a graph in the plane so that the vertices of the graph are rectangles that are aligned with the axes, and the edges of the graph are horizontal or vertical linesofsight. Such a drawing ..."
Abstract

Cited by 21 (8 self)
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We study the problem of drawing a graph in the plane so that the vertices of the graph are rectangles that are aligned with the axes, and the edges of the graph are horizontal or vertical linesofsight. Such a drawing
Universal 3Dimensional Visibility Representations for Graphs
, 1997
"... This paper studies 3dimensional visibility representations of graphs in which objects in 3d correspond to vertices and vertical visibilities between these objects correspond to edges. We ask which classes of simple objects are universal, i.e. powerful enough to represent all graphs. In particul ..."
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Cited by 19 (6 self)
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This paper studies 3dimensional visibility representations of graphs in which objects in 3d correspond to vertices and vertical visibilities between these objects correspond to edges. We ask which classes of simple objects are universal, i.e. powerful enough to represent all graphs. In particular, we show that there is no constant k for which the class of all polygons having k or fewer sides is universal. However, we show by construction that every graph on n vertices can be represented by polygons each having at most 2n sides. The construction can be carried out by an O(n ) algorithm. We also study the universality of classes of simple objects (translates of a single, not necessarily polygonal object) relative to cliques Kn and similarly relative to complete bipartite graphs Kn;m .
Planar Upward Tree Drawings with Optimal Area
 Internat. J. Comput. Geom. Appl
, 1996
"... Rooted trees are usually drawn planar and upward, i.e., without crossings and without any parent placed below its child. In this paper we investigate the area requirement of planar upward drawings of rooted trees. We give tight upper and lower bounds on the area of various types of drawings, and pro ..."
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Cited by 19 (4 self)
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Rooted trees are usually drawn planar and upward, i.e., without crossings and without any parent placed below its child. In this paper we investigate the area requirement of planar upward drawings of rooted trees. We give tight upper and lower bounds on the area of various types of drawings, and provide lineartime algorithms for constructing optimal area drawings. Let T be a boundeddegree rooted tree with N nodes. Our results are summarized as follows: ffl We show that T admits a planar polyline upward grid drawing with area O(N ), and with width O(N ff ) for any prespecified constant ff such that 0 ! ff ! 1. ffl If T is a binary tree, we show that T admits a planar orthogonal upward grid drawing with area O(N log log N ). ffl We show that if T is ordered, it admits an O(N log N)area planar upward grid drawing that preserves the lefttoright ordering of the children of each node. ffl We show that all of the above area bounds are asymptotically optimal in the worst case. ffl ...
On a Visibility Representation for Graphs in Three Dimensions
, 1993
"... Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. Application areas such as VLSI wire routing and circuit board layout have stimulated research on visibility representations where the sets belong to R². Here, ..."
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Cited by 17 (7 self)
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Visibility representations of graphs map vertices to sets in Euclidean space and express edges as visibility relations between these sets. Application areas such as VLSI wire routing and circuit board layout have stimulated research on visibility representations where the sets belong to R². Here, motivated by the emerging research area of graph drawing, we study a 3dimensional visibility representation. In this
TriangleFree Planar Graphs as Segment Intersection Graphs
 JOURNAL OF GRAPH ALGORITHMS AND APPLICATIONS
, 2002
"... We prove that every trianglefree planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross, i.e., intersect in a common interior point. Th ..."
Abstract

Cited by 17 (0 self)
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We prove that every trianglefree planar graph is the intersection graph of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross, i.e., intersect in a common interior point. This particular class of intersection graphs is also known as contact graphs.
An Experimental Comparison of Three Graph Drawing Algorithms (Extended Abstract)
, 1995
"... In this paper we present an extensive experimental study... ..."
Abstract

Cited by 15 (5 self)
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In this paper we present an extensive experimental study...