Discrete Ricci flow for geometric routing

Jie Gao Xianfeng David Gu Feng Luo

Numerical Analysis and Scientific Computing mathscidoc:1912.43798

1-8
The problem is concerned about computing virtual coordinates for greedy routing in a wireless ad hoc network. Consider a set of wireless nodes S densely deployed inside a geometric domain R2. Nodes within communication range can directly communicate with each other. We ask whether one can compute a set of virtual coordinates for S such that greedy routing has guaranteed delivery. In particular, each node forwards the message to the neighbor whose distance to the destination, computed under the virtual coordinates and some metric function d, is the smallest. If such a neighbor can always be found, greedy routing successfully delivers the message to the destination. The problem can be phrased as finding a greedy embedding of S in some geometric space, such that greedy routing always succeeds. In the setting of this entry, we assume that the nodes are a dense sample of the domain such that
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@inproceedings{jiediscrete,
  title={Discrete Ricci flow for geometric routing},
  author={Jie Gao, Xianfeng David Gu, and Feng Luo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205854895636362},
  pages={1-8},
}
Jie Gao, Xianfeng David Gu, and Feng Luo. Discrete Ricci flow for geometric routing. pp.1-8. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205854895636362.
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