A faster algorithm for torus embedding

Date

2007-07-05T23:12:08Z

Authors

Woodcock, Jennifer Roselynn

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Abstract

Although theoretically practical algorithms for torus embedding exist, they have not yet been successfully implemented and their complexity may be prohibitive to their practicality. We describe a simple exponential algorithm for embedding graphs on the torus (a surface shaped like a doughnut) and discuss how it was inspired by the quadratic time planar embedding algorithm of Demoucron, Malgrange and Pertuiset. We show that it is faster in practice than the only fully implemented alternative (also exponential) and explain how both the algorithm itself and the knowledge gained during its development might be used to solve the well-studied problem of finding the complete set of torus obstructions.

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Keywords

torus, obstruction, graph theory, embedding, graph, graph minor

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