Are there special cases of the problem that I know how to solve?
(a) Can I solve the problem efficiently when I ignore some of the input parameters?
(b) Does the problem become easier to solve when I set some of the input parameters to trivial values, such as 0 or 1?
(c) Can I simplify the problem to the point where I can solve it efficiently?
(d) Why can't this special-case algorithm be generalized to a wider class of inputs?
(e) Is my problem a special case of a more general problem in the catalog?