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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)
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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.
Computational geometry  a survey
 IEEE TRANSACTIONS ON COMPUTERS
, 1984
"... We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided de ..."
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Cited by 19 (3 self)
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We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided design, computer graphics, operations research, pattern recognition, robotics, and statistics. Five major problem areasconvex hulls, intersections, searching, proximity, and combinatorial optimizationsare discussed. Seven algorithmic techniques incremental construction, planesweep, locus, divideandconquer, geometric transformation, pruneandsearch, and dynamizationare each illustrated with an example.Acollection of problem transformations to establish lower bounds for geometric problems in the algebraic computation/decision model is also included.
IMPROVED COMPACT VISIBILITY REPRESENTATION OF Planar Graph via Schnyder’s Realizer
 SIAM J. DISCRETE MATH. C ○ 2004 SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS VOL. 18, NO. 1, PP. 19–29
, 2004
"... Let G be an nnode planar graph. In a visibility representation of G,eachnodeofG is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of G are vertically visible to each other. In the present paper we give the best known compact visibility repre ..."
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Cited by 6 (1 self)
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Let G be an nnode planar graph. In a visibility representation of G,eachnodeofG is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of G are vertically visible to each other. In the present paper we give the best known compact visibility representation of G. Given a canonical ordering of the triangulated G, our algorithm draws the graph incrementally in a greedy manner. We show that one of three canonical orderings obtained �from Schnyder’s � realizer for the triangulated G yields a visibility representation of G no wider than 22n−40. Our easytoimplement O(n)time algorithm bypasses the complicated subroutines for 15 fourconnected components and fourblock trees required by the best previously known algorithm of Kant. Our result provides a negative answer to Kant’s open question about whether � � 3n−6 is a 2 worstcase lower bound on the required width. Also, if G has no degreethree (respectively, degreefive) internal node, then our visibility representation for G is no wider than � �
On a visibility representation of graphs
 IN [41
, 1996
"... We give a visibility representation of graphs which extends some very wellknown representations considered extensively in the literature. Concretely, the vertices are represented by a collection of parallel hyperrectangles in R n and the visibility is orthogonal to those hyperrectangles. With thi ..."
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Cited by 6 (0 self)
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We give a visibility representation of graphs which extends some very wellknown representations considered extensively in the literature. Concretely, the vertices are represented by a collection of parallel hyperrectangles in R n and the visibility is orthogonal to those hyperrectangles. With this generalization, we can prove that each graph admits a visibility representation. But, it arises the problem of determining the minimum Euclidean space where such representation is possible. We consider this problem for concrete wellknown families of graphs such as planar graphs, complete graphs and complete bipartite graphs.
Further results on bar kvisibility graphs
, 2005
"... A bar visibility representation of a graph G is a collection of horizontal bars in the plane corresponding to the vertices of G such that two vertices are adjacent if and only if the corresponding bars can be joined by an unobstructed vertical line segment. In a bar kvisibility graph, two vertices ..."
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Cited by 4 (0 self)
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A bar visibility representation of a graph G is a collection of horizontal bars in the plane corresponding to the vertices of G such that two vertices are adjacent if and only if the corresponding bars can be joined by an unobstructed vertical line segment. In a bar kvisibility graph, two vertices are adjacent if and only if the corresponding bars can be joined by a vertical line segment that intersects at most k other bars. Bar kvisibility graphs were introduced by Dean, Evans, Gethner, Laison, Safari, and Trotter in [3],[4]. In this paper, we present sharp upper bounds on the maximum number of edges in a bar kvisibility graph on n vertices and the largest order of a complete bar kvisibility graph. We also discuss regular bar kvisibility graphs and forbidden induced subgraphs of bar kvisibility graphs.