Min-wise Independent Permutations: Theory and Practice

Abstract

A family of permutations F⊆S _n (the symmetric group) is called min-wise independent if for any set F⊆ [n] and any x ∈X, when a permutation π is chosen at random in F we have

$$ \Pr \left( {\min \{ \pi (X)\} = \pi (x)} \right) = \frac{1} {{\left| X \right|}}. $$

In other words we require that all the elements of any fixed set X have an equal chance to become the minimum element of the image of X under π.

The rigorous study of such families was instigated by the fact that such a family (under some relaxations) is essential to the algorithm used by the AltaVista Web indexing software to detect and filter near-duplicate documents. The insights gained from theoretical investigations led to practical changes, which in turn inspired new mathematical inquiries and results.

This talk will review the current research in this area and will trace the interplay of theory and practice that motivated it.