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Nowadays data centers are becoming huge facilities with hundreds of thousands of nodes, connected through a network. The design of such interconnection networks involves finding graph models that have good topological properties and that allow the use of efficient routing algorithms. Cayley Graphs, a kind of graphs that represents an algebraic group, meet these properties and therefore have been proposed as a model for these networks. In this paper we present a routing algorithm based on Shortlex Automatic Structure, which can be used on any interconnection network with an underlying Cayley Graph (of some finite group). We show that our proposal computes the shortest path between any two vertices with low time and space complexity in comparison with traditional routing algorithms.