• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Hyperbolic geometry of networks.
【24h】

Hyperbolic geometry of networks.

机译：网络的双曲几何。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The concept of curvature of communication networks is investigated through the theory of δ-hyperbolic space, which can be intuitively viewed as the generalization of Riemannian manifolds with negative curvature to metric graphs. The hyperbolic measure δ can be expressed in terms of slimness, insize, thinness, and fatness of geodesic triangles in the metric space. The analytical formula for the slimness, insize, thinness, and fatness are computed in terms of the internal angles of the geodesic triangles and the curvature κ of the underlying Riemannian manifold with constant negative curvature κ. In addition, the fatness of a geodesic triangle with acute angles only can be given a billiard dynamics interpretation, in the sense that the optimum inscribed triangle is the period three orbit of the billiard dynamics on a geodesic triangular table.; To assess the hyperbolic property of communication networks, the mathematical expectation of δ over the diameter for several random graph generators is computed by Monte Carlo simulation. Among random graphs, small world graphs, and scale free generators, the scale free model, which is used as a topology generator in communication network, appears to be the most hyperbolic. This result is an extra piece of evidence of the hyperbolic property of the internet which has already been claimed by two different groups, using other arguments, though.; With the evidence of the δ-hyperbolic property of the internet, multi-path routing can be achieved along quasi-geodesics, which can be computed via k-local geodesic paths. It turns out that the alternative paths are sufficiently close to the optimum path. To assess the closeness between geodesic and quasi-geodesics, an upper bound on the Hausdorff distance between the geodesic and quasi-geodesics is derived for Riemannian manifolds with constant negative curvature and general δ-hyperbolic geodesic spaces.
机译：通过δ-双曲空间理论研究了通信网络的曲率概念，该理论可以直观地视为具有负曲率的黎曼流形对度量图的推广。双曲度量δ可以用度量空间中测地线三角形的纤细，大小，纤细和脂肪表示。根据测地线三角形的内角和具有恒定负曲率κ的基础黎曼流形的曲率κ来计算纤细，尺寸，厚度和脂肪的解析公式。另外，从最佳的内接三角形是在测地线三角台上的台球动力学的周期三轨道的意义上来说，仅可以给具有锐角的测地线三角形的肥胖度提供台球动力学解释。为了评估通信网络的双曲性质，通过蒙特卡洛仿真计算了几个随机图生成器的δ直径的数学期望。在随机图，小世界图和无标度生成器中，被用作通信网络中的拓扑生成器的无标度模型似乎是最双曲线的。这个结果是互联网双曲线性质的又一证据，不过，两个不同的团体已经使用其他论据对其进行了宣称。有了互联网的δ双曲性质的证据，可以沿着准大地测量学实现多径路由，这可以通过 k 局部测地学路径来计算。事实证明，替代路径足够接近最佳路径。为了评估测地线与准测地线之间的接近度，对于具有恒定负曲率和一般δ双曲测地线空间的黎曼流形，推导了测地线与准测地线之间Hausdorff距离的上限。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号