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Abstract

It has been recently shown that any graph of genus g > 0 can be stochastically embedded into a distribution over planar graphs, with distortion O(log(g + 1)) [Sidiropoulos, FOCS 2010]. This embedding can be computed in polynomial time, provided that a drawing of the input graph into a genus-g surface is given.

We show how to compute the above embedding without having such a drawing. This implies a general reduction for solving problems on graphs of small genus, even when the drawing into a small genus surface is unknown. To the best of our knowledge, this is the first result of this type.

Keywords

Polynomial Time Span Tree Planar Graph Input Graph Auxiliary Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yury Makarychev
    • 1
  • Anastasios Sidiropoulos
    • 1
  1. 1.Toyota Technological Institute at ChicagoUSA

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