Routing in Generalized Geometric Inhomogeneous Random Graphs

Abstract

In this paper we study a new random graph model that we denote ($\kappa ,\pi$)-KG and new greedy routing algorithms (of deterministic and probabilistic nature). The ($\kappa ,\pi$)-KG graphs have power-law degree distribution and small-world properties. ($\kappa ,\pi$)-KG roots on the Geometric Inhomogeneous Random Graph (GIRG) model, and hence they both preserve the properties of the hyperbolic graphs and avoid the problems of using hyperbolic cosines. In order to construct ($\kappa ,\pi$)-KG graphs, we introduce two parameters $\kappa$ and $\pi$ in the process of building a ($\kappa ,\pi$)-KG graph. With these parameters we can generate Kleinberg and power-law networks as especial cases of ($\kappa ,\pi$)-KG. Also, we propose two new greedy routing algorithms to reduce the fail ratio and maintaining a good routing performance. The first algorithm is deterministic and the second is, in essence, a weighted random walk. We use simulation techniques to test our network model, and evaluate the new routing algorithms on the two graph models (GIRG and ($\kappa ,\pi$)-KG). In our simulations, we evaluate the number of hops to reach a destination from a source and the routing fail ratio, and measure the impact of the parameters ($\kappa$ and $\pi$) on the performance of the new routing algorithms. We observe that our graph model ($\kappa ,\pi$)-KG is more flexible than GIRG, and the new routing algorithms have better performance than the routing algorithms previously proposed.

This submission is a short paper. This work was partially funded by the Spanish grant TIN2017-88749-R (DiscoEdge), the Region of Madrid EdgeData-CM program (P2018/TCS-4499), and the NSF of China grant 61520106005.