Succinct Greedy Graph Drawing in the Hyperbolic Plane

TL;DR

This paper introduces an efficient method for creating succinct, greedy graph drawings in the hyperbolic plane that enable simple, effective geometric routing suitable for resource-constrained networks.

Contribution

The authors present a novel algorithm for hyperbolic graph drawing that supports greedy routing with succinct vertex representations, improving routing efficiency and storage.

Findings

Supports greedy geometric routing in hyperbolic plane

Vertex positions can be represented with O(log n) bits

Enables efficient routing in sensor networks

Abstract

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, in 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.