Can We Locally Compute Sparse Connected Subgraphs?

How can we solve optimization problems on data that is so large, that we cannot hope to view more than a miniscule fraction of it? When attempting to solve optimization problems on big data, we are presented with a double catastrophe, as both the inputs to and the outputs from the computation are large. One ray of hope is that often, the portion of the output that is needed by the user is, in fact, of a more manageable size. In such a situation, it would be useful if one could find very fast ways of computing only the portion of the output that is required by the user.

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