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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The traditional approach to representing tree structures is as a rooted, directed graph with the root node at the top of the page and children nodes below the parent node with lines connecting them (Figure 1). Knuth (1968, p. 305-313) has a long discussion about this standard representation, especially why the root is at the top and he offers several alternatives including brief mention of a space-filling approach. However, the remainder of his presentation and most other discussions of trees focus on various node and edge representations. By contrast, this paper deals with a two-dimensional (2-d) space-filling approach in which each node is a rectangle whose area is proportional to some attribute such as node size. This article summarises the current state of research into multiple tree visualisations. It discusses the spectrum of current representation techniques used on single trees, pairs of trees and finally multiple trees, in order to identify which representations are best suited to particular tasks and to find gaps in the representation space, in which opportunities for future multiple tree visualisation research may exist. The application areas from where multiple tree data are derived are enumerated, and the distinct structures that multiple trees make in combination with each other and the effect on subsequent approaches to their visualisation are discussed, along with the basic high-level goals of existing multiple tree visualisations.