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One-vs-one
The alternative to one-vs-all is training a model for each pair of classes. The complexity is no longer linear (it's O(n2) indeed), and the right class is determined by a majority vote. In general, this choice is more expensive and should only be adopted when a full dataset comparison is not preferable.
If you want to learn more about multiclass strategies implemented by scikit-learn, visit http://scikit-learn.org/stable/modules/multiclass.html.