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Finding a Maximum-Genius Graph Imbedding

Furst, Merrick L.; Gross, Jonathan L.; McGeoch, Lyle A.

The computational complexity of constructing the imbeddings of a given graph into surfaces of different genus is not well-understood. In this paper, topological methods and a reduction to linear matroid parity are used to develop a polynomial-time algorithm to find a maximum-genus cellular imbedding. This seems to be the first imbedding algorithm for which the running time is not exponential in the genus of the imbedding surface.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-263-87
Published Here
November 28, 2011