Greedy routing optimisation in hyperbolic networks

Abstract

Finding the optimal embedding of networks into low-dimensional hyperbolic spaces is a challenge that received considerable interest in recent years, with several different approaches proposed in the literature. In general, these methods take advantage of the exponentially growing volume of the hyperbolic space as a function of the radius from the origin, allowing a (roughly) uniform spatial distribution of the nodes even for scale-free small-world networks, where the connection probability between pairs decays with hyperbolic distance. One of the motivations behind hyperbolic embedding is that optimal placement of the nodes in a hyperbolic space is widely thought to enable efficient navigation on top of the network. According to that, one of the measures that can be used to quantify the quality of different embeddings is given by the fraction of successful greedy paths following a simple navigation protocol based on the hyperbolic coordinates. In the present work, we develop an optimisation scheme for this score in the native disk representation of the hyperbolic space. This optimisation algorithm can be either used as an embedding method alone, or it can be applied to improve this score for embeddings obtained from other methods. According to our tests on synthetic and real networks, the proposed optimisation can considerably enhance the success rate of greedy paths in several cases, improving the given embedding from the point of view of navigability.

Hyperbolic-Embedding-Aided Geographic Routing in Intelligent Vehicular Networks

“…And the D-Mercator method for the multidimensional hyperbolic embedding of real networks is designed in [40]. These hyperbolic embedding algorithms have been implemented in numerous kinds of downstream application tasks, such as community discovery [41,42], link prediction [43,44] and network routing [27,28,[45][46][47][48], which proves their efficiency and effectiveness.…”

“…The paper [47] presented hyperbolic embedding algorithms that are well-suited for greedy routing and demonstrated that hyperbolic embedding can facilitate maximally efficient greedy routing in complex networks. In [48], the authors developed an optimization scheme for improving the greedy routing score in the hyperbolic space. Inspired by these works, in this paper, we present and implement a hyperbolic-embedding-aided greedy routing strategy for performance enhancement in intelligent vehicular networks.…”