In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi treemap. To achieve this, we define a new distance function and neighborhood relationship between sites so that space will be divided by axis-aligned segments. Then a sweepline+skyline based heuristic algorithm is proposed to allocate the partitioned spaces to form an orthogonal Voronoi diagram with orthogonal rectangles. To the best of our knowledge, it is the first time to use a sweepline-based strategy for the Voronoi treemap. Moreover, we design a novel strategy to initialize the diagram status and modify the status update procedure so that the generation of our plot is more effective and efficient. We show that the proposed algorithm has an O(nlog(n)) complexity which is the same as the state-of-the-art Voronoi treemap. To this end, we show via experiments on the artificial dataset and real-world dataset the performance of our algorithm in terms of computation time, converge rate, and aspect ratio. Finally, we discuss the pros and cons of our method and make a conclusion.
Implicit hierarchy visualization methods that partition the whole space without considering the sites are treated as non-site-based methods, such as the treemap. These methods position the data by following some rules or experience in order to get expected configurations, which sometimes are also named as heuristic-based algorithm. Starting from the propose of original treemap in 1992 @cite_12 , a large number of variants are proposed in the literature @cite_11 @cite_23 .
@cite_23 @cite_12 @cite_11
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Space-filling visualization techniques have proved their capability in visualizing large hierarchical structured data. However, most existing techniques restrict their partitioning process in vertical and horizontal direction only, which cause problem with identifying hierarchical structures. This paper presents a new space-filling method named Angular Treemaps that relax the constraint of the rectangular subdivision. The approach of Angular Treemaps utilizes divide and conquer paradigm to visualize and emphasize large hierarchical structures within a compact and limited display area with better interpretability. Angular Treemaps generate various layouts to highlight hierarchical sub-structure based on user's preferences or system recommendations. It offers flexibility to be adopted into a wider range of applications, regarding different enclosing shapes. Preliminary usability results suggest user's performance by using this technique is improved in locating and identifying categorized analysis tasks. This paper presents work in progress on a new technique for visu- alising and manipulating large hierarchies. The information slices approach compactly visualises hierarchical structures using a series of semi-circular discs. The technique is described in the context of our early experience with a prototype file system visualiser based on information slices. Over the last few years, the emerging field of information visuali- sation has resulted in a numerous techniques for helping visualise and make sense of large information spaces (10). Among these are several techniques for visualising and interacting with large hierar- chies which go beyond the traditional approach taken in 2d scrolling browsers such as the Windows Explorer. Treemaps (6, 9) are space-filling visualisations of hierarchies based on successive horizontal and vertical subdivision of screen rectangles. The area of each rectangle is proportional to some at- tribute of the underlying hierarchy such as the (total) size of each subtree. Xdu (4) is a utility for the X window system which displays a graphical disk usage for Unix file systems. Rectangles are stacked from left to right as the directory tree is descended. The current di- rectory is represented by the leftmost rectangle, which is the entire height of the window. Subdirectories are represented by neighbour- ing rectangles in the next column, whose height are proportional to the size of each subdirectory. The hyperbolic browser (7) uses a focus and context technique based on hyperbolic geometry. A hierarchy is laid out uniformly on the hyperbolic plane and then mapped to the unit disc for display on screen. Nodes in the centre of the disc are largest and nodes are assigned progressively less space towards the perimeter of the disc. Cheops (3) is based on multiple re-use of overlaid triangles in the display. Working top-down, the selection of a node (triangle) at a particular level designates that node's children are to be represented Apart from explicit node-link representations, implicit visualizations and especially the Treemap as their frontrunner have acquired a solid position among the available techniques to visualize hierarchies. Their advantage is a highly space-efficient graphical representation that does not require explicit drawing of edges. In this paper, we survey the design space for this class of visualization techniques. We establish the design space along the four axes of dimensionality, edge representation, node representation, and layout by examining existing implicit hierarchy visualization techniques. The survey is completed by casting some light into regions of the design space that have not yet been explored. Our design space is not a mere theoretical construct, but a practically usable tool for rapid visualization development. To that end, we discuss a software implementation of the introduced design space. The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map.