A faster algorithm for torus embedding

• Main Author: Woodcock, Jennifer Roselynn
• Other Authors: Myrvold, Wendy
• Language: English; en
• Published: 2007
• Subjects: torus; obstruction; graph theory; embedding; graph; graph minor; UVic Subject Index::Sciences and Engineering::Applied Sciences::Computer science
• Online Access: http://hdl.handle.net/1828/130

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.