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An Algorithm for Accurate and Simple-Looking Metaphorical Maps

Authors Eleni Katsanou , Tamara Mchedlidze , Antonios Symvonis , Thanos Tolias

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Graph theory
  • Theory of computation → Graph algorithms analysis
Keywords
  • Metaphorical maps
  • contact representation
  • accuracy (cartographic error)
  • simplicity (polygon complexity)
  • force directed algorithm

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Abstract

Metaphorical maps or contact representations are visual representations of vertex-weighted graphs that rely on the geographic map metaphor. The vertices are represented by countries, the weights by the areas of the countries, and the edges by contacts/boundaries among them. The accuracy with which the weights are mapped to areas and the simplicity of the polygons representing the countries are the two classical optimization goals for metaphorical maps. Mchedlidze & Schnorr [Mchedlidze and Schnorr, 2022] presented a force-based algorithm that creates metaphorical maps that balance between these two optimization goals. Their maps look visually simple, but the accuracy of the maps is far from optimal - the countries' areas can vary up to 30% compared to required. In this paper, we provide a multi-fold extension of the algorithm in [Mchedlidze and Schnorr, 2022]. More specifically:  
1) Towards improving accuracy: We introduce the notion of region stiffness and suggest a technique for varying the stiffness based on the current pressure of map regions. 
2) Towards maintaining simplicity: We introduce a weight coefficient to the pressure force exerted on each polygon point based on whether the corresponding point appears along a narrow passage. 
3) Towards generality: We cover, in contrast to [Mchedlidze and Schnorr, 2022], non-triangulated graphs. This is done by either generating points where more than three regions meet or by introducing holes in the metaphorical map.  We perform an extended experimental evaluation that, among other results, reveals that our algorithm is able to construct metaphorical maps with nearly perfect area accuracy with a little sacrifice in their simplicity.

Cite As Get BibTex

Eleni Katsanou, Tamara Mchedlidze, Antonios Symvonis, and Thanos Tolias. An Algorithm for Accurate and Simple-Looking Metaphorical Maps. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.40

Author Details

Eleni Katsanou
  • National Technical University of Athens, Greece
Tamara Mchedlidze
  • Utrecht University, The Netherlands
Antonios Symvonis
  • National Technical University of Athens, Greece
Thanos Tolias
  • National Technical University of Athens, Greece

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References

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