Balanced Circle Packings for Planar Graphs
Md. Jawaherul Alam, David Eppstein, Michael T. Goodrich, Stephen G., Kobourov, and Sergey Pupyrev
TL;DR
This paper investigates balanced circle packings for planar graphs, focusing on the ratio of circle sizes, and presents various results on the existence of such configurations.
Contribution
It introduces new results on the existence and limitations of balanced circle packings for planar graphs, with both positive and negative findings.
Findings
Balanced packings with polynomial size ratios are possible for some planar graphs.
Certain planar graphs do not admit balanced circle contact representations.
The paper establishes bounds on the size ratios for balanced packings.
Abstract
We study balanced circle packings and circle-contact representations for planar graphs, where the ratio of the largest circle's diameter to the smallest circle's diameter is polynomial in the number of circles. We provide a number of positive and negative results for the existence of such balanced configurations.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Structural Analysis and Optimization