Planarizing an Unknown Surface
Data Structures and Algorithms
2012-06-22 v1 Computational Geometry
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 Olog (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.
Cite
@article{arxiv.1206.4898,
title = {Planarizing an Unknown Surface},
author = {Yury Makarychev and Anastasios Sidiropoulos},
journal= {arXiv preprint arXiv:1206.4898},
year = {2012}
}
Comments
The conference version of this paper will appear in the Proceedings of APPROX 2012