Succinct Greedy Graph Drawing in the Hyperbolic Plane [article]

David Eppstein, Michael T. Goodrich
2008 arXiv   pre-print
We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed geometrically, simply by having each vertex that receives M pass it along to any neighbor that is closer in the hyperbolic metric to the message's eventual destination. More importantly, for networking applications, our algorithm produces succinct drawings,
more » ... that each of the vertex positions in one of our embeddings can be represented using O(log n) bits and the calculation of which neighbor to send a message to may be performed efficiently using these representations. These properties are useful, for example, for routing in sensor networks, where storage and bandwidth are limited.
arXiv:0806.0341v1 fatcat:wntdkv5slffxtftaz5rwrizbiq