Results 1  10
of
104
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 520 (40 self)
 Add to MetaCart
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 92 (8 self)
 Add to MetaCart
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.
On the Computational Complexity of Upward and Rectilinear Planarity Testing (Extended Abstract)
, 1994
"... A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical se ..."
Abstract

Cited by 82 (4 self)
 Add to MetaCart
A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment, and no two edges cross. Testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures. In this paper we show that upward planarity testing and rectilinear planarity testing are NPcomplete problems. We also show that it is NPhard to approximate the minimum number of bends in a planar orthogonal drawing of an nvertex graph with an O(n 1\Gammaffl ) error, for any ffl ? 0.
A Better Heuristic for Orthogonal Graph Drawings
 COMPUT. GEOM. THEORY APPL
, 1998
"... An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is ben ..."
Abstract

Cited by 61 (6 self)
 Add to MetaCart
An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is bent at most twice. In particular for nonplanar and nonbiconnected planar graphs, this is a big improvement. The algorithm is very simple, easy to implement, and it handles both planar and nonplanar graphs at the same time.
A Bayesian Paradigm for Dynamic Graph Layout
, 1997
"... Dynamic graph layout refers to the layout of graphs that change over time. These changes are due to user interaction, algorithms, or other underlying processes determining the graph. Typically, users spend a noteworthy amount of time to get familiar with a layout, i.e. ..."
Abstract

Cited by 52 (13 self)
 Add to MetaCart
Dynamic graph layout refers to the layout of graphs that change over time. These changes are due to user interaction, algorithms, or other underlying processes determining the graph. Typically, users spend a noteworthy amount of time to get familiar with a layout, i.e.
Embedding Planar Graphs at Fixed Vertex Locations
, 1999
"... Let G be a planar graph of n vertices, v1 ; : : : ; vn , and let fp1 ; : : : ; png be a set of n points in the plane. We present an algorithm for constructing in O(n ) time a planar embedding of G, where vertex v i is represented by point p i and each edge is represented by a polygonal curve ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
Let G be a planar graph of n vertices, v1 ; : : : ; vn , and let fp1 ; : : : ; png be a set of n points in the plane. We present an algorithm for constructing in O(n ) time a planar embedding of G, where vertex v i is represented by point p i and each edge is represented by a polygonal curve with O(n) bends (internal vertices.) This bound is asymptotically optimal in the worst case. In fact, if G is a planar graph containing at least m pairwise independent edges and the vertices of G are randomly assigned to points in convex position, then, almost surely, every planar embedding of G mapping vertices to their assigned points and edges to polygonal curves has at least m=20 edges represented by curves with at least m=40 bends.
Parallel transitive closure and point location in planar structures
 SIAM J. COMPUT
, 1991
"... Parallel algorithms for several graph and geometric problems are presented, including transitive closure and topological sorting in planar stgraphs, preprocessing planar subdivisions for point location queries, and construction of visibility representations and drawings of planar graphs. Most of th ..."
Abstract

Cited by 23 (11 self)
 Add to MetaCart
Parallel algorithms for several graph and geometric problems are presented, including transitive closure and topological sorting in planar stgraphs, preprocessing planar subdivisions for point location queries, and construction of visibility representations and drawings of planar graphs. Most of these algorithms achieve optimal O(log n) running time using n = log n processors in the EREW PRAM model, n being the number of vertices.
Graph drawing aesthetics and the comprehension of UML class diagrams: an empirical study
, 2001
"... Many existing automatic graph layout algorithms are unrelated to any particular semantic domain. Designers of such algorithms tend to conform to layout aesthetics, and claim that by doing so, the resultant diagram is easy to understand. Few algorithms are designed for a specific domain, and there is ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
Many existing automatic graph layout algorithms are unrelated to any particular semantic domain. Designers of such algorithms tend to conform to layout aesthetics, and claim that by doing so, the resultant diagram is easy to understand. Few algorithms are designed for a specific domain, and there is no guarantee that the aesthetics used for generic layout algorithms will be useful for the visualisation of domainspecific diagrams (for example, visual programs, or entityrelationship diagrams). This paper describes a study which aimed to identify the most important aesthetics for the automatic layout of UML class diagrams from a human comprehension point of view. The results suggest that for specific domains, the actual semantics of the given graph may need to be considered before an appropriate graph drawing can be produced. ! Keywords: UML class diagrams, graph layout aesthetics, human performance.
Graph Layout Aesthetics in UML Diagrams: User Preferences
 J. Graph Algorithms Appl
, 2002
"... The merit of automatic graph layout algorithms is typically judged by their computational efficiency and the extent to which they conform to aesthetic criteria (for example, minimising the number of crossings, maximising orthogonality). Experiments investigating the worth of such algorithms from the ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
The merit of automatic graph layout algorithms is typically judged by their computational efficiency and the extent to which they conform to aesthetic criteria (for example, minimising the number of crossings, maximising orthogonality). Experiments investigating the worth of such algorithms from the point of view of human usability can take different forms, depending on whether the graph has meaning in the real world, the nature of the usability measurement, and the effect being investigated (algorithms or aesthetics). Previous studies have investigated performance on abstract graphs with respect to both aesthetics and algorithms, finding support for reducing the number of crossings and bends, and increasing the display of symmetry. This paper reports on preference experiments assessing the effect of individual aesthetics in the application domain of UML diagrams. Subjects’ preferences for one diagram over another were collected as quantitative data. Their stated reasons for their choice were collected as qualitative data. Analysis of this data enabled us to produce a priority listing of aesthetics for this domain. These UML preference results reveal a difference in aesthetic priority from those of previous domainindependent experiments.
The Techniques of Komolgorov and Bardzin for Three Dimensional Orthogonal Graph Drawings
, 1995
"... This paper appears as Technical Report 9507, Department of Computer Science, University of Newcastle, Newcastle NSW 2308 Australia. ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
This paper appears as Technical Report 9507, Department of Computer Science, University of Newcastle, Newcastle NSW 2308 Australia.