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.
In this section, we give an overview of implicit hierarchy visualization methods which are related to our work. We mainly focus on the canvas subdivision strategies used to generate layouts, instead of including all implicit visualization techniques. Based on whether the sites are referred to during the subdivision, we divide the methods into two clusters: non-site-based methods and site-based methods. Both of them belong to methods with inclusion edge representation according to the design space definition @cite_31 .
@cite_31
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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.