Di Battista, G., Eades, P., Tamassia R. and I.G. Tollis, Algorithms for Automatic Graph Drawing: An Annotated Bibliography, Brown Univ., Tech. Rep., 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... trees, another well studied class of tree drawings [20, 10] Note that the problem of constructing drawings with large angles (high resolution drawings) has been studied in [18, 7] For an up to date overview on graph drawing problems, applications, and algorithms, the reader is referred to [5]. Another application is concerned with pattern recognition. A classical way for associating a shape to a given distribution of points on the plane is to connect pairs of points that are deemed close by some proximity measure, computing in this way a graph, called a proximity graph, associated ....

G. Di Battista, P. Eades, R. Tamassia and I.G. Tollis. Algorithms for Automatic Graph Drawing: An Annotated Bibliography. To appear in Computational Geometry: Theory and Applications.

....and discs, and provide bounds on the complete graphs and complete bipartite graphs that admit such representations. 1 Introduction The problem of drawing or establishing di erent representations of a given graph has been studied extensively in the literature (see the paper of Di Battista et al.[2] for a survey of the research and applications of graph drawing) In particular, determining a visibility McGill University, Canada; jit mu .cs.mcgill.ca, romanik opus.cs.mcgill.ca, sue cs.mcgill.ca Universit e du Qu ebec a Montr eal, Canada; hazel math.uqam.ca Universit at zu K oln, ....

....Wismath [6] showed that every planar graph admits a visibility representation. Dean and Hutchinson [1] proved that K 8 is the largest complete graph that admits a visibility representation in this model. For a comprehensive overview of the various visibility representations studied, see [2]. Motivated by the results on 2 dimensional visibility representations such as the ones described above, we study a 3 dimensional visibility representation de ned as follows. Consider an arrangement of closed, disjoint rectangles in R such that the planes determined by the rectangles are ....

Di Battista, G., Eades, P., Tamassia, R., and Tollis, I.G., Algorithms for Automatic Graph Drawing: An Annotated Bibliography, Technical Report, Dept. of Computer Science, Brown University, 1993.

....of graphs, Lubiw and Sleumer [16] proved that maximal outerplanar graphs can be drawn both as relative neighborhood and Gabriel graphs. For a thorough overview on graph drawing problems and algorithms, the reader is referred to the excellent bibliography of Di Battista, Eades, Tamassia and Tollis [4]. In this paper, we study the problem of determining whether trees can be drawn as certain types of proximity graphs. A tree T can be drawn as a proximity graph when there exists a set of points in the plane such that the proximity graph of that set of points is isomorphic to T . It is known ....

G. Di Battista, P. Eades, R. Tamassia and I.G. Tollis. Algorithms for Automatic Graph Drawing: An Annotated Bibliography. To appear in Computational Geometry: Theory and Applications.

....be drawn as a minimum spanning tree. Trees that can be drawn as sphere of influence graphs were characterized by Jacobson et al. [15] For a thorough overview on graph drawing problems and algorithms, the reader is referred to the excellent bibliography of Di Battista, Eades, Tamassia and Tollis [6]. We study the proximity graph drawability problem for trees. We give a complete characterization of trees that can be drawn as (1) relative neighborhood graphs, 2) relatively closest graphs, 3) gabriel graphs and (4) modified gabriel graphs. A brief overview of the results contained in the ....

G. Di Battista, P. Eades, R. Tamassia and I.G. Tollis. Algorithms for Automatic Graph Drawing: An Annotated Bibliography. To appear in Computational Geometry: Theory and Applications.

....algorithm is based on the canonical ordering. This ordering can also be used to compute more compact visibility representations for this class of planar graphs. 1 Introduction The problem of drawing a graph on the plane has received increasing attention due to a large number of applications [3]. Examples include VLSI layout, algorithm animation, visual languages and CASE tools. Vertices are usually represented by points and edges by curves. In the design of floor planning of electronic chips and in architectural design, it is also common to represent a graph G by a rectangular dual, ....

Eades, P., and R. Tamassia, Algorithms for Automatic Graph Drawing: An Annotated Bibliography, Dept. of Comp. Science, Brown Univ., Technical Report CS-89-09, 1989.

.... 2 having symmetry. We therefore make some simplifying assumptions and rely on heuristics that run quickly and make good layouts in common cases. For a survey of other aesthetic principles, we refer the reader to the annotated bibliography on graph drawing algorithms by Eades and Tamassia [ET]. 1.2 Problem description The input to the drawing algorithm is an attributed graph G = V , E) possibly containing loops and multi edges. We assume that G is connected, as each connected component can be laid out separately. The attributes are: xsize(v) ysize(v) Size of bounding box of a ....

Eades, P. and Roberto Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography," Technical Report CS-89-09 (Revised Version), Brown University, Department of Computer Science, Providence RI, October 1989.

....graph is a drawing where the vertices are located at distinct grid points, and the edges are represented by straight line segments. Such embeddings on reasonably small grids are very useful in visualizing planar graphs on graphic screens and have applications in CAD CAM and Computer Graphics [6]. Wagner [24] F ary [8] and Stein [22] independently showed that every planar graph has a straight line embedding. Since then, many embedding algorithms have been reported (e.g. 23, 2, 16] The earlier algorithms all suffer two serious drawbacks that render them useless in practice, as noted ....

P. Eades and R. Tamassia, Algorithms for automatic graph drawing: an annotated bibliography, Technical Report, Department of Computer Science, Brown University, 1993.

....Algorithms for drawing such graphs automatically are known [Battista et al. 89] The implementation of such algorithms are typically stored as methods in abstract view classes higher up in the view class hierarchy. There is a rich source of literature available on graph drawing algorithms[Eades Tamassia 89] However, all drawing techniques are not well suited for the human visual perception system [Hubel 88] Care should be taken when selecting one since some algorithms do not preserve any spatial sorting order. A minor change among the relations in the knowledge base may cause a drastic change in ....

P. Eades, R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography", Technical Report CS-89-09, Dept. of Computer Science, Brown Univ. 1989.

....on how to solve them. Section 6 is a conclusion. 2 Visualizing Huge Hierarchies 2. 1 Exponential Explosion in Size There exist many interactive visual systems which display hierarchical structures as trees on video displays[22, 20] In general, such systems use conventional tree layout algorithms[24, 15, 3], which lay out nodes as economically and attractively as possible based on the size of node and the offset between nodes. The width of the tree, however, increases exponentially corresponding to the depth of the tree. Consider, for example, an N branch tree in 2D (Figure 1) d n 1 d n Figure 1: ....

P. Eades and R. Tamassia. Algorithms for automatic graph drawing: An annotated bibliography. Technical Report 82, Dept. of Computer Science, Univ. of Queensland, 1987.

....Drawing 5.1 Introduction 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. For a survey on graph drawing, see [36]. While this area has recently received increasing attention (see, e.g. 10,30,45,46,62,75,98] the study of drawing graphs in a dynamic setting has been an open problem. Previous work [77] only considers trees and presents a technique that restructures the drawing of a tree in time proportional ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography," Dept. of Computer Science, Brown Univ., Technical Report CS-89-09, 1989.

.... the following list is a small representative sample of the main classes of graph based models of computa2 Providing efficient algorithms that produce readable graph layouts for applications such as graph based visual programming environments is a difficult problem and an active area of research [ET89] 15 tion. It illustrates how widespread the use of a graph abstraction is in models of software systems. Petri Nets: A well known simple example of a graph based model is Petri Nets [Pet81] The Petri Net model is a parallel model of computation which is used to model the coordinated ....

....The Appendix provides a short summary of these extension packages. These widgets support the display of connected objects (nodes and links) Efficient layout algorithms for graphs, which are needed for these displays have also been the subject of extensive research [GDr93,DH89,ET89] A basic requirement for supporting the interconnection paradigm for GBVL programming environments is good support for such graph displays. Good support includes the ability to perform fast automatic layout of nodes and links of arbitrary sizes, the display of ports, the labeling of nodes, links ....

[Article contains additional citation context not shown here]

P. Eades and R. Tamassia. Algorithms for automatic graph drawing: an annotated bibliography. Tech Report CS-89-09, Dept. of Comp. Sci., Brown Univ., 1989.

.... trees, another well studied class of tree drawings [19, 9] Note that the problem of constructing drawings with large angles (high resolution drawings) has been studied in [17, 6] For an up to date overview on graph drawing problems, applications, and algorithms, the reader is referred to [4]. Finally, proximity drawing problems may be viewed as visibility problems: two points are mutually visible if a certain region between them contains no other point. From this point of view, the results in this paper deal with the problem of determining whether a tree can be realized as the ....

....a single vertex of degree 5 and its neighbors is both (fi) and [fi] drawable for these ranges of fi. The proof of statement S[7] is similar to that of S(11) statements S(7) down to S(6) follow from Lemma 4. Lemma 1, along with the results on T (1) of [2] imply the truth statements S(4) and S[4]. Statement S[3] is just Corollary 2. Theorem 4 and Theorem 3 directly imply statements S(3) down to S[1] Finally, statement S(1) can be proved by observing that every graph which is (0) drawable is a clique, and the only trees which are cliques are the trees on 1 and 2 vertices. 2 6 A ....

G. Di Battista, P. Eades, R. Tamassia and I.G. Tollis. Algorithms for Automatic Graph Drawing: An Annotated Bibliography. Computational Geometry: Theory and Applications 4, 1994, pp. 235-282.

....problem of area minimization of grid visibility for hierarchically planar graphs is generally NP hard, even restricted to s t graphs. Keywords: Graph Drawing, Hierarchically Planar Graph, Straight Line Drawing, Visibility Representation, Drawing Area. 1 Introduction Automatic graph drawing [2, 5, 13, 14, 15, 16, 17, 18] plays an important role in many computerbased applications such as CASE tools, software and information visualization, VLSI design, visual data mining, and internet navigation. Directed acyclic graphs are an important class [2] of graphs to be investigated in this area. The upward drawing ....

....1 Introduction Automatic graph drawing [2, 5, 13, 14, 15, 16, 17, 18] plays an important role in many computerbased applications such as CASE tools, software and information visualization, VLSI design, visual data mining, and internet navigation. Directed acyclic graphs are an important class [2] of graphs to be investigated in this area. The upward drawing convention for drawing acyclic directed graphs has received a great deal of attention since last decade; and a number of results for drawing upward planar graphs have been published [2, 4, 6, 11] 1 Consider [7, 8, 9, 19] that ....

[Article contains additional citation context not shown here]

G. Di Battista, P. D. Eades, R. Tamassia, and I. Tollis, Algorithms for Automatic Graph Drawing: An Annotated Bibliography, Computational Geometry: Theory and Application, 4, 235-282, 1994.

....amendment 1, and by NSF Presidential Young Investigator Award CCR 8906419, with matching funds from IBM Corporation. 1 Overview The problem of constructing drawings of graphs has important applications to circuit layout and data presentation. A survey of graph drawing algorithms appears in [2,3]. In this paper we consider planar orthogonal grid drawings, or, simply layouts, which are planar drawings such that the edges are polygonal chains consisting of horizontal and vertical segments, and the vertices and bends of the edges have integer coordinates. In numerous VLSI and graphics ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography," Networks (to appear).

....amendment 1, and by NSF Presidential Young Investigator Award CCR 8906419, with matching funds from IBM Corporation. 1 Overview The problem of constructing drawings of graphs has important applications to circuit layout and data presentation. A survey of graph drawing algorithms appears in [2,3]. In this paper we consider planar orthogonal grid drawings, or, simply layouts, which are planar drawings such that the edges are polygonal chains consisting of horizontal and vertical segments, and the vertices and bends of the edges have integer coordinates. In numerous VLSI and graphics ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography," Dept. of Computer Science, Brown Univ., Technical Report CS-89-09, 1989.

....Corporation, by the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014 83 K 0146 and ARPA order 6320, amendment 1, by the Texas Advanced Research Program under Grant No. 3972, and by the U.S. Army Research Office under grant DAAL03 91G 0035. pears in [5,6]. In this paper we consider planar orthogonal grid drawings, or, simply layouts, which are planar drawings such that the edges are polygonal chains consisting of horizontal and vertical segments, and the vertices and bends of the edges have integer coordinates. A specific survey on algorithms for ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography, " Networks (to appear).

....Corporation, by the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014 83 K 0146 and ARPA order 6320, amendment 1, by the Texas Advanced Research Program under Grant No. 3972, and by the U.S. Army Research Office under grant DAAL03 91G 0035. pears in [5,6]. In this paper we consider planar orthogonal grid drawings, or, simply layouts, which are planar drawings such that the edges are polygonal chains consisting of horizontal and vertical segments, and the vertices and bends of the edges have integer coordinates. A specific survey on algorithms for ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography, " Dept. of Computer Science, Brown Univ., Technical Report CS-89-09, 1989.

....of an acyclic digraph has all the edges flowing in the same direction, e.g. from bottom to top. A visibility representation maps vertices into horizontal segments and edges into vertical segments that intersect only the two corresponding vertex segments. Graph drawing algorithms are surveyed in [52]. In the following we denote with n and m the number of vertices and edges of a given graph. Cohen et al. 44] describe a framework for dynamic graph drawing algorithms. At a first glance, it appears that updating a drawing may require Omega Gamma n m) time in the worst case, since one may have ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography, " Dept. of Computer Science, Brown Univ., Technical Report CS-89-09, 1989.

.... CNR) 1 Introduction 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. For a survey on graph drawing, see [15]. While this area has recently received increasing attention (see, e.g. 3,10,18,19,25,28, 36] the study of drawing graphs in a dynamic setting has been an open problem. Previous work [29] only considers trees and presents a technique that restructures the drawing of a tree in time proportional ....

P. Eades and R. Tamassia, "Algorithms for Automatic Graph Drawing: An Annotated Bibliography, " Dept. of Computer Science, Brown Univ., Technical Report CS-89-09, 1989.

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Di Battista, G., Eades, P., Tamassia R. and I.G. Tollis, Algorithms for Automatic Graph Drawing: An Annotated Bibliography, Brown Univ., Tech. Rep., 1993.

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