平面化未知曲面
Planarizing an Unknown Surface
摘要：
最近已经证明，亏格g>0的任何图都可以随机嵌入到平面图上的分布中，失真为Olog（g+1））[Sidiropoulos，FOCS 2010]。这种嵌入可以在多项式时间内计算，只要给出输入图到亏格g曲面的绘图。我们展示了如何在没有这样的绘图的情况下计算上述嵌入。这意味着一个一般的减少解决问题的图的小亏格，即使在绘制成一个小亏格表面是未知的。据我们所知，这是第一个这种类型的结果。
英文摘要：
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.
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