Orthogonal Voronoi Diagram and Treemap Article Swipe

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Yanchao Wang , Feng Lin , Hock Soon Seah ·

YOU? · · 2019 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1904.02348

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.

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Theoretical Computer Science

Data Mining

Mathematics

Artificial Intelligence

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Voronoi diagram Centroidal Voronoi tessellation Computer science Skyline Plot (graphics) Heuristic Hierarchy Computation Diagram Tree (set theory) Algorithm Theoretical computer science Data mining Mathematics Artificial intelligence Combinatorics Geometry Statistics Database Market economy Economics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1904.02348
PDF: https://arxiv.org/pdf/1904.02348
OA Status: green
Cited By: 6
References: 32
Related Works: 10
OpenAlex ID: https://openalex.org/W2930719122

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DOI: https://doi.org/10.48550/arxiv.1904.02348

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Title: Orthogonal Voronoi Diagram and Treemap

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Type: preprint

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Language: en

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Publication year: 2019

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Publication date: 2019-04-04

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Authors: Yanchao Wang, Feng Lin, Hock Soon Seah

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Landing page: https://arxiv.org/abs/1904.02348

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PDF URL: https://arxiv.org/pdf/1904.02348

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Concepts: Voronoi diagram, Centroidal Voronoi tessellation, Computer science, Skyline, Plot (graphics), Heuristic, Hierarchy, Computation, Diagram, Tree (set theory), Algorithm, Theoretical computer science, Data mining, Mathematics, Artificial intelligence, Combinatorics, Geometry, Statistics, Database, Market economy, Economics

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Cited by: 6

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Citations by year (recent): 2024: 1, 2023: 1, 2022: 1, 2020: 2, 2019: 1

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References (count): 32

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cited_by_percentile_year
countries_distinct_count	1
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citation_normalized_percentile