1. Artificial Intelligence for Games Depth limited search Patrick Olivier p.l.olivier@ncl.ac.uk

2. Recap: Breadth-first search

3. Roadmap of Romania…

4. Class Exercise – Uniform-Cost Uniform-cost search –Cost to get to a node g(n) –Expand the least-cost unexpanded node –Implement with fringe ordered by path cost Romanian holiday: –Initial state: Arad –Goal state: Bucharest –Do a uniform cost search by hand

5. Recap: Depth-first search

6. Depth-limited search depth-first search with depth limit L nodes at depth L have no successors

7. Iterative deepening search to a depth limit L if no solution research to limit L+1 previous search repeated

8. Iterative deepening search: L = 0

9. Iterative deepening search: L = 1

10. Iterative deepening search: L = 2

11. Iterative deepening search: L = 3

12. Iterative deepening search Number of nodes generated in a depth-limited search to depth d with branching factor b: –N DLS = b 0 + b 1 + b 2 + … + b d-2 + b d-1 + b d Number of nodes generated in an iterative deepening search to depth d with branching factor b: –N IDS = (d+1)b 0 + d.b 1 + (d-1)b 2 + … + 3b d-2 +2b d-1 + 1b d For b=10, d=5: –N DLS = 1 + 10 + 100 + 1,000 + 10,000 + 100,000 = 111,111 –N IDS = 6 + 50 + 400 + 3,000 + 20,000 + 100,000 = 123,456 Overhead = (123,456 - 111,111)/111,111 = 11%

13. Properties of iterative deepening Complete? –Yes Time: –(d+1)b 0 + d b 1 + (d-1)b 2 + … + b d = O(b d ) Space: –O(bd) Optimal? –If the cost is the same per step

14. Summary of uninformed search