In 2D? 3D? <10D? In high-dimensional space? Binary, continuous, or count vectors, or a mix? Or something more novel? What's your distance or similarity method

In 2D? 3D? <10D? In high-dimensional space? Binary, continuous, or count vectors, or a mix? Or something more novel? What's your distance or similarity method? Is there a bound to your search? Exact or approximate? If approximate, what counts as good enough? All of these affect "optimal".