Input: graph , sink , desired subproblem number , a feasible decomposition method
Output: a set of subproblems
(1) ;
(2) apply on ;
(3) while   do
(4)let be an arbitrary element of , remove from ;
(5) apply on ;
(6)if   then
//  is a tree
(7)add to ;
(8)else
(9);
(10) ;
(11) return  ;
Algorithm 1: generate_sufficient_subproblems.