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Deriving Tidy Drawings of Trees
, 1995
"... The treedrawing problem is to produce a `tidy' mapping of elements of a tree to points in the plane. In this paper, we derive an efficient algorithm for producing tidy drawings of trees. The specification, the starting point for the derivations, consists of a collection of intuitively appealing cri ..."
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Cited by 6 (4 self)
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The treedrawing problem is to produce a `tidy' mapping of elements of a tree to points in the plane. In this paper, we derive an efficient algorithm for producing tidy drawings of trees. The specification, the starting point for the derivations, consists of a collection of intuitively appealing criteria satisfied by tidy drawings. The derivation shows constructively that these criteria completely determine the drawing. Indeed, the criteria completely determine a simple but inefficient algorithm for drawing a tree, which can be transformed into an efficient algorithm using just standard techniques and a small number of inventive steps. The algorithm consists of an upwards accumulation followed by a downwards accumulation on the tree, and is further evidence of the utility of these two higherorder tree operations.
Effects of Sociogram Drawing Conventions and Edge Crossings in Social Network Visualization
 Journal of Graph Algorithms and Applications
, 2007
"... This paper describes a withinsubjects experiment. In this experiment, the effects of different spatial layouts on human sociogram perception are examined. We compare the relative effectiveness of five sociogram drawing conventions in communicating underlying network substance, based on user task pe ..."
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Cited by 6 (0 self)
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This paper describes a withinsubjects experiment. In this experiment, the effects of different spatial layouts on human sociogram perception are examined. We compare the relative effectiveness of five sociogram drawing conventions in communicating underlying network substance, based on user task performance and personal preference. We also explore the impact of edge crossings, a widely accepted readability aesthetic. Both objective performance and subjective questionnaire measures are employed in the study. Subjective data are gathered based on the methodology of Purchase et al. [70], while objective data are collected through an online system. We found that 1) both edge crossings and drawing conventions pose significant effects on user preference and task performance of finding groups, but neither has much impact on the perception of actor status. On the other hand, node positioning and angular resolution may be more important in perceiving actor status. In visualizing social networks, it is important to note that the techniques that are highly preferred by users do not necessarily lead to best task performance. 2) subjects have a strong preference of placing nodes on the top or in the center to highlight importance, and clustering nodes in the same group and separating clusters to highlight groups. They have tendency to believe that nodes on the top or in the center are more important, and nodes in close proximity belong to the same group. Some preliminary recommendations for sociogram design and hypotheses about human reading behavior are proposed.
Tree Drawings on the Hexagonal Grid
"... We consider straightline drawings of trees on a hexagonal grid. The hexagonal grid is an extension of the common grid with inner nodes of degree six. We restrict the number of directions used for the edges fromeachnodetoitschildrenfromonetofive, andtofivepatterns: straight, Y, ψ, X, and full. The ψ ..."
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Cited by 3 (1 self)
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We consider straightline drawings of trees on a hexagonal grid. The hexagonal grid is an extension of the common grid with inner nodes of degree six. We restrict the number of directions used for the edges fromeachnodetoitschildrenfromonetofive, andtofivepatterns: straight, Y, ψ, X, and full. The ψ–drawings generalize hv or strictly upward drawings to ternary trees. Weshowthatcompleteternarytreeshavea ψ–drawingonasquareofsize O(n 1.262) and general ternary trees can be drawn within O(n 1.631) area. Bothboundsareoptimal.Sub–quadraticboundsarealsoobtainedfor X– pattern drawings of complete tetra trees, and for full–pattern drawings of complete penta trees, which are 4–ary and 5–ary trees. These results parallel and complement the ones of Frati [8] for straight–line orthogonal drawings of ternary trees. Moreover, we provide an algorithm for compacted straight–line drawings of penta trees on the hexagonal grid, such that the direction of the edges from a node to its children is given by our patterns and these edges have the same length. However, drawing trees on a hexagonal grid within a prescribed area or with unit length edges is NP–hard.
SWAN: A Data Structure Visualization System 1
"... Swan is a data structure visualization system. It allows users to visualize the data structures and execution process of a C/C++ program. Swan views a data structure as a graph or collection of graphs. By “graph ” we mean general ..."
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Swan is a data structure visualization system. It allows users to visualize the data structures and execution process of a C/C++ program. Swan views a data structure as a graph or collection of graphs. By “graph ” we mean general
A Linear Algorithm for Compact BoxDrawings of Trees
 University of Lethbridge
, 2002
"... In a boxdrawing of a tree each node is drawn by a rectangular box of prescribed size, no two boxes overlap each other, all boxes corresponding to siblings of the tree have the same xcoordinate at their left sides, and a parent node is drawn at a given distance apart from its rst child. A box draw ..."
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In a boxdrawing of a tree each node is drawn by a rectangular box of prescribed size, no two boxes overlap each other, all boxes corresponding to siblings of the tree have the same xcoordinate at their left sides, and a parent node is drawn at a given distance apart from its rst child. A box drawing of a tree is compact if it attains the minimum possible rectangular area enclosing the drawing. We give a lineartime algorithm for nding a compact boxdrawing of a tree. A known algorithm does not always nd a compact boxdrawing and takes time O(n ) if a tree has n nodes.
Drawing Unordered Trees on kGrids
"... Abstract. We present almost linear area bounds for drawing complete trees on the octagonal grid. For 7ary trees we establish an upper and lower bound of Θ(n 1.129) and for ternary trees the bounds of O(n 1.048) and Θ(n), where the latter needs edge bends. We explore the unit edge length and area co ..."
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Abstract. We present almost linear area bounds for drawing complete trees on the octagonal grid. For 7ary trees we establish an upper and lower bound of Θ(n 1.129) and for ternary trees the bounds of O(n 1.048) and Θ(n), where the latter needs edge bends. We explore the unit edge length and area complexity of drawing unordered trees on kgrids with k ∈ {4, 6, 8} and generalize the N Phardness results of the orthogonal and hexagonal grid to the octagonal grid. 1
Display of Sensor Networks: a Feasibility Study
, 2006
"... 2. Improvement of the existing tree layout...........................................................................................3 2.1. Mapping of the tree using general tree drawing algorithms................................. 3 2.1.1. Problem description......................................... ..."
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2. Improvement of the existing tree layout...........................................................................................3 2.1. Mapping of the tree using general tree drawing algorithms................................. 3 2.1.1. Problem description........................................................................................3 2.1.2. Walker's algorithm......................................................................................... 3