Search by partial solutions

 nodes are partial or complete states  graphs are DAGs (may be trees) source (root) is empty state sinks (leaves) are complete states  directed edges represent setting parameter values

4 queens: separate row and column complete solutions possible pruning

Implications of partial solutions  pruning of “impossible” partial solutions  need partial evaluation function

Partial Solution Trees and DAGs  trees: search might use tree traversal methods based on BFS, DFS advantage: depth is limited! (contrast to complete solution space)  DAGs: spanning trees

Partial solution algorithms  greedy  divide and conquer  dynamic programming  branch and bound  A*

Greedy algorithm  make best ‘local’ parameter selection at each step: complete solutions

Greedy SAT  partial evaluation  order of setting propositions T/F P = {P 1, P 2,…,P n } f(P) = D 1  D 2 ...  D k e.g., D i = P f  ~P g  P h How much pre-processing?

Greedy TSP  partial evaluation  order of adding edges Cities: C 1, C 2,…,C n symmetric distances How much preprocessing? C1C1 C2C2 C2C2

Branch and bound  Avoid traversing paths to complete solutions based on partial evaluation  Does not avoid exponential performance

4 queens: separate row and column complete solutions possible pruning More in next slide set…