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OST: a heuristic-based orthogonal partitioning algorithm for dynamic hierarchical data visualization

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Abstract

Tools for intuitive visualization of dynamic datasets are highly demanded for capturing information and revealing potential patterns, especially in understanding the trend of data changes. We propose a novel resolution-independent heuristic algorithm, termed Orthogonal Stable Treemap (OST), to implicitly display dynamic hierarchical data value changes. OST adopts a site-based method as the Voronoi treemap (VT), to preserve the layout stability for diversified data values. Meanwhile, OST partitions the whole canvas with horizontal or vertical lines, instead of the lines with arbitrary orientations in VT. Technical innovations are made in three parts: Initialization of site state to speed up the algorithm and preserve the layout; efficient computation of orthogonal rectangular diagram to partition the empty canvas; self-adaption of site state to quickly reach an equilibrium. The performance of OST is quantitatively evaluated in terms of computation complexity, computation time, convergence rate, visibility, and stability. Moreover, qualitative evaluations (use case and user study) are demonstrated on the dynamic work-in-process dataset in the wafer fab. Evaluation results show that OST combines the advantages of layout stability and tidiness, contributing to easier and faster plot understanding.

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References

  • Armitage J (2014) Method and system for generating a columnar tree map. 8854371. https://www.freepatentsonline.com/8854371.html

  • Auber D, Huet C, Lambert A, Renoust B, Sallaberry A, Saulnier A (2013) Gospermap: using a gosper curve for laying out hierarchical data. IEEE Trans Visual Comput Graphics 19(11):1820–1832

    Article  Google Scholar 

  • Aurenhammer F (1987) Power diagrams: properties, algorithms and applications. SIAM J Comput 16(1):78–96

    Article  MathSciNet  Google Scholar 

  • Aurenhammer F, Edelsbrunner H (1984) An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recogn 17(2):251–257

    Article  MathSciNet  Google Scholar 

  • Balzer M, Deussen O (2005) Voronoi treemaps. In: Proc. INFOVIS. IEEE, pp 49–56

  • Bederson BB, Shneiderman B, Wattenberg M (2002) Ordered and quantum treemaps: making effective use of 2d space to display hierarchies. ACM Trans Graphics 21(4):833–854

    Article  Google Scholar 

  • Bethge J, Hahn S, Döllner J (2017) Improving layout quality by mixing treemap-layouts based on data-change characteristics. In: Proceedings of the conference on vision, modeling and visualization, pp 69–76

  • Bostock M, Ogievetsky V, Heer J (2011) \(\text{ D}^3\) data-driven documents. IEEE Trans Visual Comput Graphics 17(12):2301–2309

    Article  Google Scholar 

  • Bruls M, Huizing K, Van Wijk JJ (2000) Squarified treemaps. In: Data visualization 2000. Springer, pp 33–42

  • Burch M, Konevtsova N, Heinrich J, Hoeferlin M, Weiskopf D (2011) Evaluation of traditional, orthogonal, and radial tree diagrams by an eye tracking study. IEEE Trans Visual Comput Graphics 17(12):2440–2448

    Article  Google Scholar 

  • Burke EK, Kendall G, Whitwell G (2004) A new placement heuristic for the orthogonal stock-cutting problem. Oper Res 52(4):655–671

    Article  Google Scholar 

  • Chen Y, Du X, Yuan X (2017) Ordered small multiple treemaps for visualizing time-varying hierarchical pesticide residue data. Vis Comput 33(6–8):1073–1084

    Article  Google Scholar 

  • de Berg M, Speckmann B, van der Weele V (2014) Treemaps with bounded aspect ratio. Comput Geom 47(6):683–693

    Article  MathSciNet  Google Scholar 

  • Du Q, Faber V, Gunzburger M (1999) Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev 41(4):637–676

    Article  MathSciNet  Google Scholar 

  • Duarte FS, Sikansi F, Fatore FM, Fadel SG, Paulovich FV (2014) Nmap: a novel neighborhood preservation space-filling algorithm. IEEE Trans Visual Comput Graphics 20(12):2063–2071

    Article  Google Scholar 

  • Feng C, Gong M, Deussen O, Huang H (2019) Treemapping via balanced partitioning. Proc. computational visual media (CVM’19)

  • Fiedler C, Scheibel W, Limberger D, Trapp M, Döllner J (2020) Survey on user studies on the effectiveness of treemaps. In: Proceedings of the 13th international symposium on visual information communication and interaction, pp 1–10

  • Fischer F, Fuchs J, Mansmann F (2012) Clockmap: enhancing circular treemaps with temporal glyphs for time-series data. In: Eurographics conference on visualization. Eurographics Association, pp 97–101

  • Fortune S (1987) A sweepline algorithm for Voronoi diagrams. Algorithmica 2(1–4):153

    Article  MathSciNet  Google Scholar 

  • Gavrilova M (1998) Proximity and applications in general metrics. Ph.D. thesis, University of Calgary

  • Ghoniem M, Cornil M, Broeksema B, Stefas M, Otjacques B (2015) Weighted maps: treemap visualization of geolocated quantitative data. In: Visualization and data analysis 2015, vol 9397. International Society for Optics and Photonics, p 93970

  • Görtler J, Schulz C, Weiskopf D, Deussen O (2018) Bubble treemaps for uncertainty visualization. IEEE Trans Visual Comput Graphics 24(1):719–728

    Article  Google Scholar 

  • Gotz D (2011) Dynamic voronoi treemaps: a visualization technique for time-varying hierarchical data. Phys Rev A 30(2):150–156

    Google Scholar 

  • Graham M, Kennedy J (2010) A survey of multiple tree visualisation. Inf Vis 9(4):235–252

    Article  Google Scholar 

  • Hahn S, Trümper J, Moritz D, Döllner J (2014) Visualization of varying hierarchies by stable layout of Voronoi treemaps. In: Proc. IVAPP. IEEE, pp 50–58

  • Itoh T, Yamaguchi Y, Ikehata Y, Kajinaga Y (2004) Hierarchical data visualization using a fast rectangle-packing algorithm. IEEE Trans Visual Comput Graphics 10(3):302–313

    Article  Google Scholar 

  • Kieffer S, Dwyer T, Marriott K, Wybrow M (2016) Hola: human-like orthogonal network layout. IEEE Trans Visual Comput Graphics 22(1):349–358

    Article  Google Scholar 

  • Kobayashi A, Misue K, Tanaka J (2012) Edge equalized treemaps. In: Proc. IV. IEEE, pp 7–12

  • Kong N, Heer J, Agrawala M (2010) Perceptual guidelines for creating rectangular treemaps. IEEE Trans Visual Comput Graphics 16(6):990–998

    Article  Google Scholar 

  • Lai Y-J, Cheng P-H, Lu L-W, Rau C-R (2015) A visualization by innovated squarified treemap for somatosensory data analysis. In: 2015 IEEE 4th global conference on consumer electronics (GCCE). IEEE, pp 587–588

  • Liang J, Nguyen QV, Simoff S, Huang ML (2012) Angular treemaps-a new technique for visualizing and emphasizing hierarchical structures. In: Proc. IV. IEEE, pp 74–80

  • Long LK, Hui LC, Fook GY, Zainon WMNW (2017) A study on the effectiveness of tree-maps as tree visualization techniques. Proc Comput Sci 124:108–115

    Article  Google Scholar 

  • Mönch L, Fowler JW, Dauzere-Peres S, Mason SJ, Rose O (2011) A survey of problems, solution techniques, and future challenges in scheduling semiconductor manufacturing operations. J Sched 14(6):583–599

    Article  MathSciNet  Google Scholar 

  • Monostori L (2014) Cyber-physical production systems: roots, expectations and r & d challenges. Procedia Cirp 17:9–13

    Article  Google Scholar 

  • Nocaj A, Brandes U (2012) Computing Voronoi treemaps: faster, simpler, and resolution-independent. In: Computer graphics forum, vol 31. Wiley Online Library, pp 855–864

  • Scheibel W, Limberger D, Döllner J (2020) Survey of treemap layout algorithms. In: Proceedings of the 13th international symposium on visual information communication and interaction, pp 1–9

  • Scheibel W, Trapp M, Limberger D, Döllner J (2020) A taxonomy of treemap visualization techniques. In: VISIGRAPP (3: IVAPP), pp 273–280

  • Scheibel W, Weyand C, Bethge J, Döllner J (2021) Algorithmic improvements on Hilbert and Moore treemaps for visualization of large tree-structured datasets

  • Scheibel W, Weyand C, Döllner J (2018) Evocells-a treemap layout algorithm for evolving tree data. In: VISIGRAPP (3: IVAPP), pp 273–280

  • Schulz H-J (2011) Treevis.net: a tree visualization reference. IEEE Comput Graphics Appl 31(6):11–15

    Article  Google Scholar 

  • Schulz H-J, Hadlak S, Schumann H (2011) The design space of implicit hierarchy visualization: a survey. IEEE Trans Visual Comput Graphics 17(4):393–411

    Article  Google Scholar 

  • Shneiderman B (1992) Tree visualization with tree-maps: 2-d space-filling approach. ACM Trans Graphics 11(1):92–99

    Article  Google Scholar 

  • Shneiderman B, Wattenberg M (2001) Ordered treemap layouts. In: Proc. INFOVIS. IEEE, pp 73–78

  • Sondag M, Speckmann B, Verbeek K (2018) Stable treemaps via local moves. IEEE Trans Visual Comput Graphics 24(1):729–738

    Article  Google Scholar 

  • Sud A, Fisher D, Lee H-P (2010) Fast dynamic Voronoi treemaps. In: Proc. ISVD. IEEE, pp 85–94

  • Tak S, Cockburn A (2013) Enhanced spatial stability with Hilbert and Moore treemaps. IEEE Trans Visual Comput Graphics 19(1):141–148

    Article  Google Scholar 

  • Tu Y, Shen H-W (2007) Visualizing changes of hierarchical data using treemaps. IEEE Trans Visual Comput Graphics 13(6):1286–1293

    Article  Google Scholar 

  • Vernier EF, Comba JLD, Telea AC (2018) A stable greedy insertion treemap algorithm for software evolution visualization. In: 2018 31st SIBGRAPI conference on graphics, patterns and images (SIBGRAPI). IEEE, pp 158–165

  • Vernier E, Sondag M, Comba J, Speckmann B, Telea A, Verbeek K (2020) Quantitative comparison of time-dependent treemaps. In: Computer graphics forum, vol 39, pp 393–404. Wiley Online Library

  • Wang YC, Liu JG, Lin F, Seah HS (2020) Generating orthogonal Voronoi treemap for visualization of hierarchical data. In: Proc. CGI. ACM

  • Wang Y, Chen L (2015) Two-dimensional residual-space-maximized packing. Expert Syst Appl 42(7):3297–3305

    Article  Google Scholar 

  • Wang G, Nakanishi T, Fukuda A (2016) 2-d layout for tree visualization: a survey. In: Proc. MATEC Web of conferences, vol 56. EDP Sciences

  • Wang W, Wang H, Dai G, Wang H (2006) Visualization of large hierarchical data by circle packing. In: Proc. CHI. ACM, pp 517–520

  • Wang Y, Zhang Q, Lin F, Seah HS (2019) Engineqv: investigating external cause of engine failures based on geo-temporal association. In: 2019 IEEE Pacific visualization symposium (PacificVis). IEEE, pp 184–188

  • Wattenberg M (2005) A note on space-filling visualizations and space-filling curves. In: Proc. INFOVIS. IEEE, pp 181–186

  • Wood J, Dykes J (2008) Spatially ordered treemaps. IEEE Trans Vis Comput Gr 14(6)

  • Zhang C, Bard JF, Chacon R (2017) Controlling work in process during semiconductor assembly and test operations. Int J Prod Res 55(24):7251–7275

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the A*STAR Cyber-Physical Production System (CPPS)-Towards Contextual and Intelligent Response Research Program, under the RIE2020 IAF-PP GrantA19C1a0018, and Model Factory @SIMTech. This work is also partially supported by a Grant MOE 2017-T1-001-053-04 from Ministry of Education, Singapore.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Nanyang Technological University, Singapore, Singapore

    Yan-Chao Wang, Feng Lin, Hock-Soon Seah & Jie Zhang

  2. Department of Biomedical Engineering, National University of Singapore, Singapore, Singapore

    Yidan Xing

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Wang, YC., Xing, Y., Lin, F. et al. OST: a heuristic-based orthogonal partitioning algorithm for dynamic hierarchical data visualization. J Vis 25, 875–896 (2022). https://doi.org/10.1007/s12650-022-00830-1

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