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Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding

机译:Schnyder Woods适用于更高属的三角表面及其在编码中的应用

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Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into three spanning trees. We extend here definitions and algorithms for Schnyder woods to closed orientable surfaces of arbitrary genus. In particular, we describe a method to traverse a triangulation of genus g and compute a so-called g-Schnyder wood on the way. As an application, we give a procedure to encode a triangulation of genus g and n vertices in 4n+O(glog (n)) bits. This matches the worst-case encoding rate of Edgebreaker in positive genus. All the algorithms presented here have execution time O((n+g)g) and hence are linear when the genus is fixed.
机译:施奈德森林是平面三角剖分的著名组合结构,可分解为三棵生成树。我们在这里将Schnyder木材的定义和算法扩展到任意属的闭合定向曲面。特别地,我们描述了一种遍历g属的三角剖分并在计算途中计算所谓的g-Schnyder木材的方法。作为一个应用程序,我们给出了一个程序,以4n + O(glog(n))位对g和n个顶点的三角剖分进行编码。这与正类Edgebreaker的最坏情况编码率匹配。这里介绍的所有算法都具有执行时间O((n + g)g),因此当属固定时是线性的。

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