2-D Layout for Tree Visualization: a survey

MATEC Web of Conferences 56, 01007 (2016) DOI: 10.1051/ matecconf/20165601007 ICCAE 2016 2-D Layout for Tree Visualization: a survey 1 2 Guanqun Wang , Tsuneo Nakanishi and Akira Fukuda 1 1 Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan 819-0395 Department of Electronics Engineering and Computer Science, Faculty of Engineering, Fukuoka University, Fukuoka, Japan 814-0180 2 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. 1 Introduction Since a major part of real world information is hierarchically structured, and tree is a perfect data structure for the storage of hierarchy information, an effective method of tree visualization becomes necessary in a lot applications. This paper will introduce new tree visualization ideas proposed recently. Although there are already some researches on 2.5D[1, 2] and 3D[3, 4] visualization of trees, to narrow down the topic, this paper will only focus on 2D tree visualization methods. For the same reason, we mainly introduce layouts in this paper and very little information about navigation or interaction techniques will be included. The researches on tree visualization started about half a century ago [5], and there have been a lot of developed approaches to visualize trees in different situations. Based on how the parent-child relationship is represented, all tree visualization methods can be roughly divided into two large groups, connection methods and enclosure methods [6, 7]. In the following part of this paper, Section 2 will introduce some widely used connection methods; Section 3 will introduce some famous enclosure methods; Section 4 will discuss about other tree visualization methods designed especially for mobile devices; Section 5 will talk about some hybrid methods. 2 Connection Methods Connection methods uses node-link diagram to explicitly show the relationships of nodes. They make it very easy for the user to get an immediate perception of the structure. However, usually they are not efficient in display space utilization [6]. The following subsections will introduce some main categories of connection methods. 2.1 Level-Based Drawing In a level-based drawing, all nodes are placed on a set of layers which are several parallel lines in the display area, and typically all nodes from the same level are placed on one unique layer. The structure is pretty explicit in such drawings. However, it usually takes a lot of efforts to improve the space utilization. Buchheim, Jünger and Leipert summarized 5 aesthetic properties which are commonly required when drawing a rooted tree [8]: - The y-coordinate of each node corresponds its level. - The edges do not cross. - The drawing of a subtree is independent of its position in the tree. - If the tree is ordered, the ordering information is shown in the drawing. - The drawing of the reflection of a tree is the reflected drawing of the original tree. In 1981, Reingold and Tilford proposed the first linear time layout algorithm satisfying all 5 aesthetics, thus it is one of the most famous tree layout algorithms and usually called Reingold-Tilford algorithm now [9]. This algorithm, in a bottom-up direction, recursively draws subtrees independently and puts subtrees with the same parent as close as possible. After all nodes have fixed coordinates, the edges are then inserted accordingly. The Reingold-Tilford algorithm was originally proposed to draw ordered binary trees, but Walker modified it later and successfully made a variation which works for general trees without violating any of the aesthetics [10]. This variation is known as Walker’s algorithm in a lot of © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). MATEC Web of Conferences 56, 01007 (2016) DOI: 10.1051/ matecconf/20165601007 ICCAE 2016 portion of the tree (focus) without sacrifice of context presentation so that it can effectively visualize a much larger tree than the conventional methods. researches. In 2002, Buchheim, Jünger and Leipert proved that Walker’s algorithm does not run in linear time like Walker claimed and presented a modification of Walker’s algorithm with linear runtime [8]. So far all variations of Reingold-Tilford algorithm place a parent at the centre of its children, which in fact, according to the research of Marriott and Sbarski, can lead to an unnecessarily large width. By relaxing the requirement of placing a parent exactly in the centre of its children and taking edge lengths into consideration during drawing, Marriott and Sbarski presented a compact version of Walker’s algorithm [11]. When the size varies from node to node, layered drawing may use more space than necessary. 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 [12–16], 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]. When we allow nodes from different levels to be placed on the same layer, we can obtain a shorter drawing and the minimum-layer drawing becomes an interesting problem. Some researches have been done on drawing graphs on two or three layers [18]. Suderman have proved optimal upper and lower bounds for h-layer drawing of trees and proposed a linear layout algorithm matching the upper bound [19]. Alam, Samee, Rabbi, and Rah- man proposed a layout algorithm for minimumlayer up- ward drawing which can run in linear time [20]. One year later, Mondal, Alam, and Rahman demonstrated a linear algorithm for general minimum-layer drawing [21]. In- stead of the pathwidth [22] used in a lot of layered drawings, these two algorithms use a new parameter called line- labelling to divide the tree, and the results are satisfying. Figure 1. (a) Horizontal composition (b) Vertical composition 2.2 Non-Level-Based Drawing Non-level-based drawings are not as good at showing structure information as level-based drawing. However, given more freedom of nodes placements, they can achieve improvements in some metrics such as angular resolution, space utilization, aspect ratio, algorithm runtime and so on. The H-V (Horizontal-Vertical) approach is one of the most well-known none-level-b (...truncated)