Editing Open Problems:68
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How many queries are needed to accomplish this task? | How many queries are needed to accomplish this task? | ||
β | When $p = 2$ and each | + | When $p = 2$ and each column has exactly two ones, $A$ can be seen as the incidence matrix of a graph, |
and its rank is equal to $n - c$, where $c$ is the number of connected components. | and its rank is equal to $n - c$, where $c$ is the number of connected components. | ||
In this case, the rank can be approximated efficiently, with $\tilde O(1/\epsilon^2)$ queries, because we know how to efficiently approximate $c$ {{cite|ChazelleRT-05}}. | In this case, the rank can be approximated efficiently, with $\tilde O(1/\epsilon^2)$ queries, because we know how to efficiently approximate $c$ {{cite|ChazelleRT-05}}. |