The Experts below are selected from a list of 213 Experts worldwide ranked by ideXlab platform
Michael Kaufmann - One of the best experts on this subject based on the ideXlab platform.
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Graph Drawing - An Interactive Tool to Explore and Improve the Ply Number of Drawings
Lecture Notes in Computer Science, 2018Co-Authors: Niklas Heinsohn, Michael KaufmannAbstract:Given a straight-line drawing \(\varGamma \) of a graph \(G=(V,E)\), for every vertex v the Ply disk \(D_v\) is defined as a disk centered at v where the radius of the disk is half the length of the longest edge incident to v. The Ply Number of a given drawing is defined as the maximum Number of overlapping disks at some point in \(\mathrm {I\!R}^2\). Here we present a tool to explore and evaluate the Ply Number for graphs with instant visual feedback for the user. We evaluate our methods in comparison to an existing Ply computation by De Luca et al. [WALCOM’17]. We are able to reduce the computation time from seconds to milliseconds for given drawings and thereby contribute to further research on the Ply topic by providing an efficient tool to examine graphs extensively by user interaction as well as some automatic features to reduce the Ply Number.
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Graph Drawing - On Vertex- and Empty-Ply Proximity Drawings
Lecture Notes in Computer Science, 2018Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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An Interactive Tool to Explore and Improve the Ply Number of Drawings
arXiv: Data Structures and Algorithms, 2017Co-Authors: Niklas Heinsohn, Michael KaufmannAbstract:Given a straight-line drawing $\Gamma$ of a graph $G=(V,E)$, for every vertex $v$ the Ply disk $D_v$ is defined as a disk centered at $v$ where the radius of the disk is half the length of the longest edge incident to $v$. The Ply Number of a given drawing is defined as the maximum Number of overlapping disks at some point in $\mathbb{R}^2$. Here we present a tool to explore and evaluate the Ply Number for graphs with instant visual feedback for the user. We evaluate our methods in comparison to an existing Ply computation by De Luca et al. [WALCOM'17]. We are able to reduce the computation time from seconds to milliseconds for given drawings and thereby contribute to further research on the Ply topic by providing an efficient tool to examine graphs extensively by user interaction as well as some automatic features to reduce the Ply Number.
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On Vertex- and Empty-Ply Proximity Drawings
arXiv: Data Structures and Algorithms, 2017Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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Graph Drawing - Low Ply Drawings of Trees
Lecture Notes in Computer Science, 2016Co-Authors: Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hancl, Antonios Symvonis, Stephen G. Kobourov, Michael Kaufmann, Pavel ValtrAbstract:We consider the recently introduced model of low Ply graph drawing, in which the Ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The Ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest Number of Ply-disks having a common overlap is called the Ply-Number of the drawing.
Pavel Valtr - One of the best experts on this subject based on the ideXlab platform.
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Graph Drawing - On Vertex- and Empty-Ply Proximity Drawings
Lecture Notes in Computer Science, 2018Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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On Vertex- and Empty-Ply Proximity Drawings
arXiv: Data Structures and Algorithms, 2017Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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Graph Drawing - Low Ply Drawings of Trees
Lecture Notes in Computer Science, 2016Co-Authors: Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hancl, Antonios Symvonis, Stephen G. Kobourov, Michael Kaufmann, Pavel ValtrAbstract:We consider the recently introduced model of low Ply graph drawing, in which the Ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The Ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest Number of Ply-disks having a common overlap is called the Ply-Number of the drawing.
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Low Ply Drawings of Trees
arXiv: Data Structures and Algorithms, 2016Co-Authors: Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hancl, Antonios Symvonis, Stephen G. Kobourov, Michael Kaufmann, Pavel ValtrAbstract:We consider the recently introduced model of \emph{low Ply graph drawing}, in which the Ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The \emph{Ply-disk} of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest Number of Ply-disks having a common overlap is called the \emph{Ply-Number} of the drawing. We focus on trees. We first consider drawings of trees with constant Ply-Number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic Ply-Number and show that trees with maximum degree $6$ always admit such drawings in polynomial area.
Stephen G. Kobourov - One of the best experts on this subject based on the ideXlab platform.
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Graph Drawing - On Vertex- and Empty-Ply Proximity Drawings
Lecture Notes in Computer Science, 2018Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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On Vertex- and Empty-Ply Proximity Drawings
arXiv: Data Structures and Algorithms, 2017Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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an experimental study on the Ply Number of straight line drawings
Workshop on Algorithms and Computation, 2017Co-Authors: Felice De Luca, Stephen G. Kobourov, Emilio Di Giacomo, Walter Didimo, Giuseppe LiottaAbstract:The Ply Number of a drawing is a new criterion of interest for graph drawing. Informally, the Ply Number of a straight-line drawing of a graph is defined as the maximum Number of overlapping disks, where each disk is associated with a vertex and has a radius that is half the length of the longest edge incident to that vertex. This paper reports the results of an extensive experimental study that attempts to estimate correlations between the Ply Numbers and other aesthetic quality metrics for a graph layout, such as stress, edge-length uniformity, and edge crossings. We also investigate the performances of several graph drawing algorithms in terms of Ply Number, and provides new insights on the theoretical gap between lower and upper bounds on the Ply Number of k-ary trees.
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WALCOM - An Experimental Study on the Ply Number of Straight-Line Drawings
WALCOM: Algorithms and Computation, 2017Co-Authors: Felice De Luca, Stephen G. Kobourov, Emilio Di Giacomo, Walter Didimo, Giuseppe LiottaAbstract:The Ply Number of a drawing is a new criterion of interest for graph drawing. Informally, the Ply Number of a straight-line drawing of a graph is defined as the maximum Number of overlapping disks, where each disk is associated with a vertex and has a radius that is half the length of the longest edge incident to that vertex. This paper reports the results of an extensive experimental study that attempts to estimate correlations between the Ply Numbers and other aesthetic quality metrics for a graph layout, such as stress, edge-length uniformity, and edge crossings. We also investigate the performances of several graph drawing algorithms in terms of Ply Number, and provides new insights on the theoretical gap between lower and upper bounds on the Ply Number of k-ary trees.
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Graph Drawing - Low Ply Drawings of Trees
Lecture Notes in Computer Science, 2016Co-Authors: Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hancl, Antonios Symvonis, Stephen G. Kobourov, Michael Kaufmann, Pavel ValtrAbstract:We consider the recently introduced model of low Ply graph drawing, in which the Ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The Ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest Number of Ply-disks having a common overlap is called the Ply-Number of the drawing.
Patrizio Angelini - One of the best experts on this subject based on the ideXlab platform.
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Graph Drawing - On Vertex- and Empty-Ply Proximity Drawings
Lecture Notes in Computer Science, 2018Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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On Vertex- and Empty-Ply Proximity Drawings
arXiv: Data Structures and Algorithms, 2017Co-Authors: Patrizio Angelini, Jaroslav Hancl, Stephen G. Kobourov, Michael Kaufmann, Felice De Luca, Niklas Heinsohn, Steven Chaplick, Jirí Fiala, Jan Kratochvíl, Pavel ValtrAbstract:We initiate the study of the vertex-Ply of straight-line drawings, as a relaxation of the recently introduced Ply Number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-Ply of a drawing is determined by the vertex covered by the maximum Number of disks. The main motivation for considering this relaxation is to relate the concept of Ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-Ply Number 1 can be seen as a weak proximity drawing, which we call empty-Ply drawing. We show non-trivial relationships between the Ply Number and the vertex-Ply Number. Then, we focus on empty-Ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the Ply and the vertex-Ply of planar drawings.
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Graph Drawing - Low Ply Drawings of Trees
Lecture Notes in Computer Science, 2016Co-Authors: Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hancl, Antonios Symvonis, Stephen G. Kobourov, Michael Kaufmann, Pavel ValtrAbstract:We consider the recently introduced model of low Ply graph drawing, in which the Ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The Ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest Number of Ply-disks having a common overlap is called the Ply-Number of the drawing.
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Low Ply Drawings of Trees
arXiv: Data Structures and Algorithms, 2016Co-Authors: Patrizio Angelini, Michael A. Bekos, Till Bruckdorfer, Jaroslav Hancl, Antonios Symvonis, Stephen G. Kobourov, Michael Kaufmann, Pavel ValtrAbstract:We consider the recently introduced model of \emph{low Ply graph drawing}, in which the Ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The \emph{Ply-disk} of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest Number of Ply-disks having a common overlap is called the \emph{Ply-Number} of the drawing. We focus on trees. We first consider drawings of trees with constant Ply-Number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic Ply-Number and show that trees with maximum degree $6$ always admit such drawings in polynomial area.
Cristian Guillermo Gebhardt - One of the best experts on this subject based on the ideXlab platform.
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simultaneous Ply order Ply Number and Ply drop optimization of laminate wind turbine blades using the inverse finite element method
Composite Structures, 2018Co-Authors: Alejandro E Albanesi, Facundo Bre, Victor D Fachinotti, Cristian Guillermo GebhardtAbstract:Abstract This paper presents a novel methodology to simultaneously determine the optimal Ply-order, Ply-Number and Ply-drop configuration of laminate wind turbine blades using simulation-based optimization, considering the shape that the laminates are expected to attain after large elastic deformations. This methodology combines Genetic Algorithms with the Inverse Finite Element Method. As an actual engineering application, we redesigned the composite stacking layout of a medium-power 40-kW wind turbine blade to reduce its weight, subjected to mechanical and manufacturing constraints such as allowable tip deflection, maximum stress, natural frequencies, and maximum Number of successive identical plies. Results demonstrate weight reductions of up to 15% compared to the initial layout, proving that the proposed methodology is a robust redesign tool capable of effectively determining the optimal composite stacking layout of laminate wind turbine blades.