A linear algorithm for compact box‐drawings of trees

Hasan, Masud; Rahman, Md. Saidur; Nishizeki, Takao

doi:10.1002/net.10092

Cited by 5 publications

(6 citation statements)

References 8 publications

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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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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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“…In [13], Hasan presents an algorithm to draw a tree in a compact form. We use this algorithm for laying out the spanning tree of unstructured fragments and extended it to support the layout of non-tree edges (cf.…”

Section: Related Workmentioning

confidence: 99%

A linear time layout algorithm for business process models

Gschwind

Pinggera

Zugal

et al. 2014

Journal of Visual Languages & Computing

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The layout of a business process model influences how easily it can be understood. Existing layout features in process modeling tools often rely on graph representations, but do not take the specific properties of business process models into account. In this paper, we propose an algorithm that is based on a set of constraints which are specifically identified toward establishing a readable layout of a process model. Our algorithm exploits the structure of the process model and allows the computation of the final layout in linear time. We explain the algorithm, show its detailed run-time complexity, compare it to existing algorithms, and demonstrate in an empirical evaluation the acceptance of the layout generated by the algorithm. The data suggests that the proposed algorithm is well perceived by moderately experienced process modelers, both in terms of its usefulness as well as its ease of use.

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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%

“…The merged right contour is the right contour of the current subtree, followed by the remainder of the right contour of the left siblings. More precisely, the merged left contour consists of the nodes [1,4,5], and the merged right contour consists of the nodes [4,5,[7][8][9]. After merging the contours, the iteration ends and the algorithm starts moving the next child subtree.…”

Section: Redefining the Tidy Tree Problemmentioning

confidence: 99%

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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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A linear algorithm for compact box‐drawings of trees

Cited by 5 publications

References 8 publications

2-D Layout for Tree Visualization: a survey

2-D Layout for Tree Visualization: a survey

A linear time layout algorithm for business process models

Drawing non-layered tidy trees in linear time

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