Depth-first layout algorithm for trees

Miyadera, Youzou; Anzai, Koushi; Unno, Hiroshi; Yaku, Takeo

doi:10.1016/s0020-0190(98)00068-4

Cited by 6 publications

(11 citation statements)

References 5 publications

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“…The best-known previous algorithm under the same set of aesthetic conditions runs in O(n 2 ) time [5], but does not always find a compact box-drawing.…”

Section: Discussionmentioning

confidence: 99%

“…Obviously, all box-drawings of a tree have the same width because of Condition (C2) and are "optimally compact in its width," that is, "optimally compact in the x-direction." Miyadera et al gave an O(n 2 ) time algorithm for finding a box-drawing of a tree [5]. Their algorithm works in two phases: In the first phase, it finds an initial box-drawing which is not always compact, but satisfies an additional constraint that the drawing areas of any two subtrees whose roots are siblings do not overlap each other.…”

Section: Preliminariesmentioning

confidence: 99%

“…In this section, we give a linear-time algorithm for finding a compact box-drawing of a tree T. It suffices to give a linear-time algorithm for finding a compact box-drawing from an arbitrary box-drawing ⌫ of T, for example, the initial box-drawing which can be found in linear time by the first phase of the algorithm in [5].…”

Section: Compact Drawingmentioning

confidence: 99%

See 2 more Smart Citations

A linear algorithm for compact box‐drawings of trees

2003

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In a box-drawing of a rooted 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 x-coordinate at their left sides, and a parent node is drawn at a given distance apart from its first child. A box drawing of a tree is compact if it attains the minimum possible rectangular area enclosing the drawing. We give a linear-time algorithm for finding a compact box-drawing of a tree. A known algorithm does not always find a compact box-drawing and takes time O(n 2 ) if a tree has n nodes.

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“…The best-known previous algorithm under the same set of aesthetic conditions runs in O(n 2 ) time [5], but does not always find a compact box-drawing.…”

Section: Discussionmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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A linear algorithm for compact box‐drawings of trees

2003

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“…In such situations, a non-layered drawing method which places children at a fixed distance from the parent may be more practical. A lot of work on non-layered drawing can be found in the existing literature [12][13][14][15][16], however, none of them gave a linear algorithm for the general case. In 2014, Ploeg proposed a non-layered variation of ReingoldTilford algorithm and proved it can run in linear time [17].…”

Section: Level-based Drawingmentioning

confidence: 99%

2-D Layout for Tree Visualization: a survey

Wang

Nakanishi

Fukuda

2016

MATEC Web of Conferences

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Abstract. This is a survey of recent researches on 2D tree visualization approaches. The whole paper will focus on 2D layouts for general trees including different styles of node-link diagram, main variations of Treemap, some solutions designed especially for mobile devices, and several hybrid approaches. We are not trying to give an exhaustive list of tree layouts here. Instead, we will introduce new ideas in the main categories of general tree layouts, which may inspire more efficient and creative designs.

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“…In our example, the left siblings have a left contour, consisting of the nodes [1,4,5], and a right contour, consisting of the nodes [3][4][5][6]. The current subtree has of a left contour, [7,8], and a right contour, [7][8][9].…”

Section: Redefining the Tidy Tree Problemmentioning

confidence: 99%

Drawing non-layered tidy trees in linear time

Ploeg

2013

Softw. Pract. Exper.

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SUMMARYThe well‐known Reingold–Tilford algorithm produces tidy‐layered drawings of trees: drawings where all nodes at the same depth are vertically aligned. However, when nodes have varying heights, layered drawing may use more vertical space than necessary. A non‐layered drawing of a tree places children at a fixed distance from the parent, thereby giving a more vertically compact drawing. Moreover, non‐layered drawings can also be used to draw trees where the vertical position of each node is given, by adding dummy nodes. In this paper, we present the first linear‐time algorithm for producing non‐layered drawings. Our algorithm is a modification of the Reingold–Tilford algorithm, but the original complexity proof of the Reingold–Tilford algorithm uses an invariant that does not hold for the non‐layered case. We give an alternative proof of the algorithm and its extension to non‐layered drawings. To improve drawings of trees of unbounded degree, extensions to the Reingold–Tilford algorithm have been proposed. These extensions also work in the non‐layered case, but we show that they then cause a O(n2) run‐time. We then propose a modification to these extensions that restores the O(n) run‐time. Copyright © 2013 John Wiley & Sons, Ltd.

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Depth-first layout algorithm for trees

Cited by 6 publications

References 5 publications

A linear algorithm for compact box‐drawings of trees

A linear algorithm for compact box‐drawings of trees

2-D Layout for Tree Visualization: a survey

Drawing non-layered tidy trees in linear time

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