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In this paper, we present a new link-state routing algorithm called Approximate Link state (XL) aimed at increasing routing efficiency by suppressing updates from parts of the network. We prove that three simple criteria for update propagation are sufficient to guarantee soundness, completeness and bounded optimality for any such algorithm. We show, via simulation, that XL significantly outperforms standard link-state and distance vector algorithms - in some cases reducing overhead by more than an order of magnitude - while having negligible impact on path length. Finally, we argue that existing link-state protocols, such as OSPF, can incorporate XL routing in a backwards compatible and incrementally deployable fashion.