Value ordering for finding all solutions

In finding all solutions to a constraint satisfaction
problem, or proving that there are none, with a
search algorithm that backtracks chronologically
and forms k-way branches, the order in which the
values are assigned is immaterial. However, we
show that if the values of a variable are assigned
instead via a sequence of binary choice points, and
the removal of the value just tried from the domain
of the variable is propagated before another value
is selected, the value ordering can affect the search
effort. We show that this depends on the problem
constraints; for some types of constraints, we show
that the savings in search effort can be significant,
given a good value ordering