An Efficient Algorithm for the Genus Problem with Explicit Construction of Forbidden Subgraphs

@inproceedings{Djidjev1991AnEA,
  title={An Efficient Algorithm for the Genus Problem with Explicit Construction of Forbidden Subgraphs},
  author={Hristo Djidjev and John H. Reif},
  booktitle={STOC},
  year={1991}
}
We give an algorithm for irnbedding a graph G of n vertices onto an oriented surface of minimum genus g. If g z O then we also construct a forbidden subgraph of G which is homecjmorphic to a graph of size exp(O(g)! ) which cannot be irnbedded on a surface of genus g-1. Our algorithm takes sequential time exp(O(g)!)nO(l). Since exp(O (g)!) = exp(exp(O (glob))), our algorithm is polynomial time for genus g= O(loglog(n)/logloglog(,m)). A simple parallel implementation of our algorithm takes… CONTINUE READING
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