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Issue No.01 - January (2011 vol.17)
pp: 101-114
Jonathan Stott , University of Kent, Canterbury
Peter Rodgers , University of Kent, Canterbury
Juan Carlos Martínez-Ovando , University of Kent, Canterbury
Stephen G. Walker , University of Kent, Canterbury
This paper describes an automatic mechanism for drawing metro maps. We apply multicriteria optimization to find effective placement of stations with a good line layout and to label the map unambiguously. A number of metrics are defined, which are used in a weighted sum to find a fitness value for a layout of the map. A hill climbing optimizer is used to reduce the fitness value, and find improved map layouts. To avoid local minima, we apply clustering techniques to the map—the hill climber moves both stations and clusters when finding improved layouts. We show the method applied to a number of metro maps, and describe an empirical study that provides some quantitative evidence that automatically-drawn metro maps can help users to find routes more efficiently than either published maps or undistorted maps. Moreover, we have found that, in these cases, study subjects indicate a preference for automatically-drawn maps over the alternatives.
Information visualization, diagram layout, graph drawing.
Jonathan Stott, Peter Rodgers, Juan Carlos Martínez-Ovando, Stephen G. Walker, "Automatic Metro Map Layout Using Multicriteria Optimization", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 1, pp. 101-114, January 2011, doi:10.1109/TVCG.2010.24
[1] "Transport for London Website,", Apr. 2005.
[2] K. Garland, Mr. Beck's Underground Map. Capital Transport Publishing, 1994.
[3] S. Anand, S. Avelar, J. Ware, and J. Jackson, "Automated Schematic Map Production Using Simulated Annealing and Gradient Descent Approaches," Proc. 15th Ann. GIS Research UK Conf. (GISRUK), 2007.
[4] R.A. Burkhard and M. Meier, "Tube Map: Evaluation of a Visual Metaphor for Interfunctional Communication of Complex Projects," Proc. Fourth Int'l Conf. Knowledge Management (I-KNOW '04), pp. 449-456, 2004.
[5] W.C. Hahn and R.A. Weinberg, "A Subway Map of Cancer Pathways," Nature Reviews Cancer, vol. 2, no. 5, May 2002.
[6] T. Bang, K. Grønbæk, and P.S. Hansen, "Using a Metro Map Metaphor for Organizing Web-Based Learning Resources," Proc. World Conf. Educational Media, Hypermedia and Telecomm. (ED-MEDIA '02), pp. 647-652, 2002.
[7] J.M. Stott and P. Rodgers, "Metro Map Layout Using Multicriteria Optimization," Proc. Information Visualization Conf. (IV '04), pp. 355-362, 2004.
[8] J.M. Stott and P. Rodgers, "Automatic Metro Map Design Techniques," Proc. 22nd Int'l Cartographic Conf., 2005.
[9] J.M. Stott, "Automatic Layout of Metro Maps Using Multicriteria Optimisation," PhD dissertation, Computing Laboratory, Univ. of Kent, 2008.
[10] S.-H. Hong, D. Merrick, and H.A.D. do Noscimento, "The Metro Map Layout Problem," Proc. Asia Pacific Symp. Information Vizualization (APVIS '04), pp. 91-100, 2004.
[11] S.-H. Hong, D. Merrick, and H.A.D. do Noscimento, "Automatic Visualisation of Metro Maps," J. Visual Languages and Computing, vol. 17, pp. 203-224, 2006.
[12] M. Nöllenburg and A. Wolff, "A Mixed Integer Program for Drawing High-Quality Metro Maps," Proc. 13th Int'l Symp. Graph Drawing (GD '05), pp. 321-333, 2005.
[13] D. Merrick and J. Gudmundsson, "Path Simplification for Metro Map Layout," Proc. 14th Int'l Symp. Graph Drawing (GD '07), pp. 258-269, 2007.
[14] M.A. Bekos, M. Kaufmann, K. Potika, and A. Symvonis, "Line Crossing Minimization on Metro Maps," Proc. 15th Int'l Symp. Graph Drawing (GD '07), pp. 231-242, 2007.
[15] M. Agrawala and C. Stolte, "Rendering Effective Route Maps: Improving Usability through Generalization," Proc. ACM SIGGRAPH '01, pp. 241-249, 2001.
[16] S. Avelar and R. Huber, "Modeling a Public Transport Network for Generation of Schematic Maps and Location Queries," Proc. 20th Int'l Cartographic Conf., pp. 1472-1480, 2001.
[17] H. Casakin, T. Barkowsky, A. Klippel, and C. Freska, "Schematic Maps as Wayfinding Aids," Proc. Int'l Conf. Spatial Cognition II, pp. 54-71, 2001.
[18] P. Yates and M. Humphries, "The Generation of Schematic Diagrams from Geographic Representations of Networks," Proc. Spatial Information Research Centre's 10th Colloquium, 1998.
[19] S. Cabello, M. de Berg, S. van Dijk, and M.J. van Kreveld, "Schematization of Road Networks," Proc. 17th Symp. Computational Geometry, pp. 33-39, 2001.
[20] U. Lauther and A. Stübinger, "Generating Schematic Cable Plans Using Spring Embedder Methods," Proc. Symp. Graph Drawing, pp. 465-466, 2001.
[21] R. Davidson and D. Harel, "Drawing Graphs Nicely Using Simulated Annealing," ACM Trans. Graphics, vol. 15, no. 4, pp. 301-331, 1996.
[22] C. Kosak, J. Marks, and S. Shieber, "A Parallel Genetic Algorithm for Network-Diagram Layout," Proc. Fourth Int'l Conf. Genetic Algorithms, pp. 458-465, 1991.
[23] H.C. Purchase, R.F. Cohen, and M. Jones, "Validating Graph Drawing Aesthetics," Proc. Symp. Graph Drawing, F.J. Brandenburg, ed., pp. 435-446, 1995.
[24] T. Barkowsky, L.J. Latecki, and K.-F. Richter, "Schematizing Maps: Simplification of Geographic Shapes by Discrete Curve Elimination," Proc. Int'l Conf. Spatial Cognition II, pp. 41-53, 2000.
[25] M. Nöllenburg, "Automated Drawing of Metro Maps," Master's thesis, Inst. für Theoretische Informatik, Univ. Karlsruhe, Aug. 2005.
[26] T. Slocum, R. McMaster, F. Kessler, and H. Howard, Thematic Cartography and Geographic Visualization. Prentice Hall, 2005.
[27] Mexico City "Sistema de Transporte Colectivo" Website, http:/, Feb. 2008.
[28] "Sydney CityRail Website," http:/, Sept. 2007.
[29] I. Vollick, D. Vogel, M. Agrawala, and A. Herzmann, "Specifying Label Layout Styles by Example," Proc. 20th ACM Symp. User Interface Software and Technology (UIST '07), pp. 221-230, Oct. 2007.
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