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37
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 587 (41 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.
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 ..."
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Cited by 22 (10 self)
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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.
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 ..."
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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 20 (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 .
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 18 (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
MultiDimensional Orthogonal Graph Drawing with Small Boxes
 Proc. 7th International Symp. on Graph Drawing (GD '99
, 1999
"... In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the Ddimensional (D >= 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane. ..."
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Cited by 14 (6 self)
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In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the Ddimensional (D >= 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane.
OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. ..."
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Cited by 12 (2 self)
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A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.
Area Requirement of Visibility Representations of Trees
, 1996
"... We study the area requirement of barvisibility and rectanglevisibility representations of trees in the plane. We prove asymptotically tight lower and upper bounds on the area of such representations, and give lineartime algorithms that construct representations with asymptotically optimal area. ..."
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Cited by 11 (7 self)
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We study the area requirement of barvisibility and rectanglevisibility representations of trees in the plane. We prove asymptotically tight lower and upper bounds on the area of such representations, and give lineartime algorithms that construct representations with asymptotically optimal area.
Unit barvisibility layouts of triangulated polygons: Extended abstract
 In Lecture Notes in Computer Science 3383: Graph Drawing
, 2005
"... Abstract. A triangulated polygon is a 2connected maximal outerplanar graph. A unit barvisibility graph (UBVG for short) is a graph whose vertices can be represented by disjoint, horizontal, unitlength bars in the plane so that two vertices are adjacent if and only if there is a nondegenerate, uno ..."
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Cited by 8 (5 self)
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Abstract. A triangulated polygon is a 2connected maximal outerplanar graph. A unit barvisibility graph (UBVG for short) is a graph whose vertices can be represented by disjoint, horizontal, unitlength bars in the plane so that two vertices are adjacent if and only if there is a nondegenerate, unobstructed, vertical band of visibility between the corresponding bars. We give combinatorial and geometric characterizations of the triangulated polygons that are UBVGs. To each triangulated polygon G we assign a character string with the property that G is a UBVG if and only if the string satisfies a certain regular expression. Given a string that satisfies this condition, we describe a lineartime algorithm that uses it to produce a UBV layout of G. 1