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Maybe this is a silly question but I actually can't fulfill that by myself. I'm reading some papers about similarity metrics and I always find that for a distance function $d$ the triangle inequality is needed in order to support in indexing techniques and to implement, for instance, nearest neighbors queries.

Thus my question is: why is that property needed? Isn't indexing possible in presence of a distance function which does not fulfill the triangle inequality?

Thanks for your insights!

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