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How to Draw a Clustered Tree
, 2007
"... The visualization of clustered graphs is a classical algorithmic topic that has several practical applications and is attracting increasing research interest. In this paper we deal with the visualization of clustered trees, a problem that is somehow foundational with respect to the one of visualizin ..."
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The visualization of clustered graphs is a classical algorithmic topic that has several practical applications and is attracting increasing research interest. In this paper we deal with the visualization of clustered trees, a problem that is somehow foundational with respect to the one of visualizing a general clustered graph. We show many, in our opinion, surprising results that put in evidence how drawing clustered trees has many sharp differences with respect to drawing “plain” trees. We study a wide class of drawing standards, giving both negative and positive results. Namely, we show that there are clustered trees that do not have any drawing in certain standards and others that require exponential area. On the contrary, for many drawing conventions there are efficient algorithms that allow to draw clustered trees with polynomial asymptotic optimal area.
PedVis: A Structured, SpaceEfficient Technique for Pedigree Visualization
, 2011
"... Public genealogical databases are becoming increasingly populated with historical data and records of the current population's ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and denser, which justif ..."
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Public genealogical databases are becoming increasingly populated with historical data and records of the current population's ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and denser, which justifies the need for using organized, spaceefficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree's structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the Htree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user's ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, userstudy results indicate potential for user acceptance of the new layout.
PROXIMITY DRAWINGS OF HIGHDEGREE TREES
, 2013
"... A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a par ..."
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A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the partition or covering satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set.
StraightLine Drawings on Restricted Integer Grids in Two and Three Dimensions
"... This paper investigates the following question: Given a grid φ, where φ is a proper subset of the integer 2D or 3D grid, which graphs admit straightline crossingfree drawings with vertices located at (integral) grid points of φ? We characterize the trees that can be drawn on a strip, i.e., on a tw ..."
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This paper investigates the following question: Given a grid φ, where φ is a proper subset of the integer 2D or 3D grid, which graphs admit straightline crossingfree drawings with vertices located at (integral) grid points of φ? We characterize the trees that can be drawn on a strip, i.e., on a twodimensional n × 2 grid. For arbitrary graphs we prove lower bounds for the height k of an n × k grid required for a drawing of the graph. Motivated by the results on the plane we investigate restrictions of the integer grid in 3D and show that every outerplanar graph with n vertices can be drawn crossingfree with straight lines in linear volume on a grid called a prism. This prism consists of 3n integer grid points and is universal – it supports all outerplanar graphs of n vertices. We also show that there exist planar graphs that cannot be drawn on the prism and that extension to an n × 2 × 2 integer grid, called a box, does not admit the entire class of planar graphs.
Comp 5901 Directed Studies JGraphEd – A Java Graph Editor and Graph Drawing Framework
, 2004
"... 2. Framework...................................................................................................................... 4 ..."
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2. Framework...................................................................................................................... 4