Fig 7. Schematic example of a subproblem of the proposed algorithm.

(A) Example subproblem ${\mathbf{L}}_{w_i,v_j}^n$: At the n ^th algorithmic step, we search for all paths of weight w _i leading to node v _j; (B) Finding a solution for the current subproblem by investigating solutions to prior subproblems: We investigate all predecessors v _p of the current node v _j; if there exists a solution to ${\mathbf{L}}_{w_p,v_p}^M$, i.e., there is a solution to the prior subproblem $v_s\stackrel{w_p}{⇝}{v}_p$ of finding a path of weight w _p leading from v _s to v _p, and w _p + w _{(vp, vj)} = w _i, we find a solution to the current subproblem ${\mathbf{L}}_{w_i,v_j}^n$.