The Galois Complexity of Graph Drawing: Why Numerical Solutions Are Ubiquitous for ForceDirected, Spectral, and Circle Packing DrawingsBannister, Michael J. and Devanny, William E. and Eppstein, David and Goodrich, Michael T. (2014) The Galois Complexity of Graph Drawing: Why Numerical Solutions Are Ubiquitous for ForceDirected, Spectral, and Circle Packing Drawings. In: Graph Drawing 22nd International Symposium, GD 2014, September 2426, 2014 , pp. 149161(Official URL: http://dx.doi.org/10.1007/9783662458037_13). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783662458037_13
AbstractMany wellknown graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of lowdegree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.
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