Greedy routing optimisation in hyperbolic networks

Area of Science:

• Network science
• Data visualization
• Computational geometry

Background:

• Hyperbolic embeddings are used to represent complex networks in low-dimensional spaces.
• These embeddings leverage hyperbolic geometry's properties for efficient node distribution and network navigation.
• Quantifying embedding quality often involves measuring the success rate of navigation protocols.

Purpose of the Study:

• To develop an optimization scheme for improving network navigability within hyperbolic embeddings.
• To enhance the success rate of greedy pathfinding algorithms using hyperbolic coordinates.
• To provide a method that can be used independently or to refine existing hyperbolic embeddings.

Main Methods:

• An optimization algorithm was developed for hyperbolic embeddings in the native disk representation.
• The algorithm optimizes the score based on the success rate of greedy paths.
• The method was tested on both synthetic and real-world network datasets.

Main Results:

• The proposed optimization scheme significantly improved the success rate of greedy paths in several tested networks.
• The method enhanced the navigability of existing hyperbolic embeddings.
• Performance gains were observed for both synthetic and real-world network structures.

Conclusions:

• The developed optimization technique effectively enhances network navigability in hyperbolic spaces.
• This method offers a valuable tool for improving the quality of hyperbolic network embeddings.
• The findings suggest practical applications in network analysis and efficient information retrieval.