1. Artificial Intelligence
Lecture 5
Uninformed Search

2. Overview
Searching for Solutions
Uninformed Search
BFS
UCS
DFS
DLS
IDS

3. Searching for Solutions

4. Tree Search Algorithms

5. Tree Search Example

6. Implementation: State vs. Nodes
and state

7. General Tree Search

8. Search Strategies

9. Uninformed Search

10. Uninformed Search Strategies
Use only the information available in the problem definition
Breadth-first search
Uniform-cost search
Depth-first search
Depth-limit search
Iterative deepening search

11. Breadth-First Search Expand shallowest unexpanded node
Implementation: fringe is a FIFO queue, that is new successors go at end

12. Properties of BFS Complete? Time? Space? Optimal?
Yes. (if b is finite)
Time?
1+b+b2+…+b(bd-1)=O(bd+1), exp in d
Space?
O(bd+1) (keeps every node in memory)
Optimal?
Yes, if cost = 1 per step; not optimal in general when actions have different cost
Space is the big problem; can easily generate nodes at 10MB/sec, so 24hrs = 860GB

13. Uniform-Cost Search

14. Depth-First Search Expanded deepest unexpanded node Implementation:
Fringe = LIFO queue, i.e. put successors at front

15. Properties of DFS Complete? Time? Space? Optimal?
No. Fails in infinite-depth spaces, spaces with loops
Modify to avoid repeated states along path => complete in finite space
Time?
O(bm), terrible if m is much larger than d, but if solutions are dense, may be much faster than BFS
Space?
O(bm), linear space
Optimal? No

16. Depth-Limit Search
Depth-first search with depth limit L, that is nodes at depth L have no successors

17. Depth-Limited search Is DF-search with depth limit l.
i.e. nodes at depth l have no successors.
Problem knowledge can be used
Solves the infinite-path problem.
If l < d then incompleteness results.
If l > d then not optimal.
Time complexity:
Space complexity:

18. Depth-Limit Search
Algorithm

19. Iterative Deepening Search
A general strategy to find best depth limit l.
Goals is found at depth d, the depth of the shallowest goal-node.
Often used in combination with DF-search
Combines benefits of DF- en BF-search

20. Iterative Deepening Search

21. Properties of IDS

22. Bidirectional search Two simultaneous searches from start an goal.
Motivation:
Check whether the node belongs to the other fringe before expansion.
Space complexity is the most significant weakness.
Complete and optimal if both searches are BF.

23. How to search backwards?
The predecessor of each node should be efficiently computable.
When actions are easily reversible.

24. Summary of Algorithms YES* NO YES, if l  d YES bd+1 bC*/e bm bl bd
Criterion
Breadth-First
Uniform-cost
Depth-First
Depth-limited
Iterative deepening
Bidirectional search
Complete?
YES* NO
YES,
if l  d
YES
Time
bd+1
bC*/e bm bl bd
bd/2
Space
Optimal?

25. Repeated States

26. Graph Search

27. Summary
Searching for Solutions
Uninformed Search
BFS
UCS
DFS
DLS
IDS