Communication complexity theory studies the following question: how many bits
of
communication are required to compute a Boolean function f whose arguments are
distributed among several parties, possibly with overlap? Apart from being a
natural subject of study in its own right, communication complexity sheds
light
on various questions in the theory of computing that do not seem to involve
communication in any way.

A function f of basic importance in the area is the so called disjointness
function, which evaluates to true when its arguments are sets with empty
intersection. The multiparty communication requirements of this function have
been studied since the late 1980s, with only very partial results available.
In
this work, we essentially resolve the question in its entirety.