1. Prof. Dechter ICS 270A Winter 2003
Lecture Notes 2
Prof. Dechter
ICS 270A
Winter 2003

2. Explicit Graph

3. Graph Theory Sates: board configurations
Operators: move-blank: up, down, right, left (when possible)

4. Graph Theory (continued)

5. Breadth-First Search (BFS) Properties
Solution Length: optimal
Search Time: O(Bd)
Memory Required: O(Bd)
Drawback: require exponential space 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6. Iterative Deepening (DFS)
Every iteration is a DFS with a depth cutoff.
Iterative deepening (ID)
i = 1
While no solution, do
DFS from initial state S0 with cutoff i
If found goal, stop and return solution, else, increment cutoff
Comments:
ID implements BFS with DFS
Only one path in memory
BFS at step i may need to keep 2i nodes in OPEN

7. Iterative Deepening (DFS)
Time:
BFS time is O(bn)
B is the branching degree
ID is asymptotically like BFS
For b=10 d=5 d=cut-off
DFS = ,…,=111,111
IDS = 123,456
Ratio is

8. Bi-Directional Search

9. Bi-Directional Search (continued)

10. Breadth First Search Put the start node s on OPEN.
If OPEN is empty exit with failure.
Remove the first node n from OPEN and place it on CLOSED.
If n is a goal node, exit successfully with the solution obtained by tracing back pointers from n to s.
Otherwise, expand n, generating all its successors attach to them pointer back to n, and put them at the end of OPEN
Go to step 2.
For shortest cost path:
5’. Otherwise, expand n, generating all its successors attach to them pointer back to n, put them at in OPEN and order OPEN based on shortest cost partial path.

11. Uniform Cost Search Expand lowest-cost OPEN node (g(n))
In BFS g(n) = depth(n)
Requirement
g(successor)(n))  g(n)

12. Comparison of Algorithms