Iterative Refinement

• The refinement of P is structured so that repeated solution of subproblem P’ eventually solves P.

/* Solve problem P */

while (P not yet been solved)

/* Solve subproblem P’ */

. . .

• Question: How can repeatedly doing P’ solve P ?

• Answer: P’ must be parameterized in terms of some state variable(s). Each execution of P’ must change the state so progress is made, i.e., with each iteration, we move to a state that is “closer” to a solution for P.

• Different notions of “distance” lead to different programs.