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One of the key features of small-worlds is the ability to route messages with few hops only using local knowledge of the topology. In 2000, Kleinberg proposed a model based on an augmented grid that asymptotically exhibits such property.

In this paper, we propose to revisit the original model from a simulation-based perspective. Our approach is fueled by a new algorithm that can draw an augmenting link in Õ(1).

The resulting speed gain enables detailed numerical evaluations. We show for example that in practice, the augmented scheme proposed by Kleinberg is more robust than predicted by the asymptotic behavior, even for very large finite grids. We also propose tighter bounds on the performance of Kleinberg's routing algorithm. At last, we show that, fed with realistic parameters, the model gives results in line with real-life experiments.