Distributed distance computation and routing with small messages

We consider shortest paths computation and related tasks from the viewpoint of network algorithms, where the n-node input graph is also the computational system: nodes represent processors and edges represent communication links, which can in each time step carry an $$\mathcal {O}(\log n)$$O(logn)-bit message. We identify several basic distributed distance computation tasks that are highly useful in the design of more sophisticated algorithms and provide efficient solutions. We showcase the utility of these tools by means of several applications.

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