1. Artificial Intelligence
Lecture 4 – Uninformed Search
Dr. Muhammad Adnan Hashmi
6 December 2018

2. Uninformed Search Strategies
Uninformed search strategies use only the information available in the problem definition
Breadth-first search
Uniform-cost search
Depth-first search
Depth-limited search
Iterative deepening search
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3. Breadth-first search Expand shallowest unexpanded node Implementation:
fringe is a FIFO queue, i.e., new successors go at end
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4. Breadth-first search Expand shallowest unexpanded node Implementation:
fringe is a FIFO queue, i.e., new successors go at end
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5. Breadth-first search Expand shallowest unexpanded node Implementation:
fringe is a FIFO queue, i.e., new successors go at end
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6. Breadth-first search Expand shallowest unexpanded node Implementation:
fringe is a FIFO queue, i.e., new successors go at end
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7. Breadth-first search
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8. Properties of Breadth-first search
Complete? Yes (if b is finite)
Time? 1+b+b2+b3+… +bd + b(bd-1) = O(bd+1)
Space? O(bd+1) (keeps every node in memory)
Optimal? Yes (if cost = 1 per step)
Space is the bigger problem (more than time).
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9. Preventing Loopy Paths
We can have search graphs (instead of trees)
Hence paths can go backwards, ABCB
Can get paths with loops ABCDB
We can also have multiple paths to a node
From them, we are interested in the min-cost path
The Loop problem is that we “rediscover” nodes that the search has already discovered
Need to consider methods to suppress nodes that have already been visited.
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10. Uniform-Cost Search
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11. A S B G C 10 1 5 5 5 15 Consider the following problem…
We wish to find the shortest route from node S to node G; that is, node S is the initial state and node G is the goal state. In terms of path cost, we can clearly see that the route SBG is the cheapest route. However, if we let breadth-first search loose on the problem it will find the non-optimal path SAG, assuming that A is the first node to be expanded at level 1.

12. Once node B has been expanded it is removed from the queue and the revealed node (node G) is added. The queue is again sorted on path cost. Note, node G now appears in the queue twice, once as G10 and once as G11. As G10 is at the front of the queue, we now proceed to goal state. Press space.
Node A is removed from the queue and the revealed node (node G) is added to the queue. The queue is again sorted on path cost. Note, we have now found a goal state but do not recognise it as it is not at the front of the queue. Node B is the cheaper node. Press space.
We now expand the node at the front of the queue, node A. Press space to continue.
Node S is removed from the queue and the revealed nodes are added to the queue. The queue is then sorted on path cost. Nodes with cheaper path cost have priority.In this case the queue will be Node A (1), node B (5), followed by node C (15). Press space.
We start with our initial state and expand it… A A 10 1 5 5 S S B B G G G G G G
The goal state is achieved and the path S-B-G is returned. In relation to path cost, UCS has found the optimal route. 15 C
Size of Queue: 3
Size of Queue: 0
Size of Queue: 1
Size of Queue: 0
Queue: G10, G11, C15
Queue: B, G11, C
Queue: Empty
Queue: S
Queue: A, B, C
Queue: Empty
Nodes expanded: 3
Nodes expanded: 1
Nodes expanded: 2
Nodes expanded: 0
Current action: Waiting….
Current action: Expanding
FINISHED SEARCH
Current action: Expanding
Current action: Backtracking
Current level: 1
Current level: n/a
Current level: 0
Current level: 0
Current level: 2
Current level: 1
UNIFORM COST SEARCH PATTERN

13. Uniform-Cost Search
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14. Uniform-Cost Search Expand least-cost unexpanded node Implementation:
fringe = queue ordered by path cost
Equivalent to breadth-first if step costs all equal
Complete? Yes, if step cost ≥ ε
Time? O(bceiling(C*/ ε)) where C* is the cost of the optimal solution
Space? O(bceiling(C*/ ε))
Optimal? Yes – given the condition of completeness – you always expand the node with lowest cost
O(bceiling(C*/ ε)) can be greater than Ob/d
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15. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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16. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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17. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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18. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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19. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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20. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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21. Depth-first search Expand deepest unexpanded node Implementation:
fringe is a LIFO queue, i.e., put successors in the front
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22. Properties of Depth-first search
Complete? No: fails in infinite-depth spaces, spaces with loops
Complete in finite spaces
Time? O(bm): terrible if m is much larger than d
But if solutions are dense, may be much faster than breadth-first
Space? O(bm), i.e., linear space!
Optimal? No
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23. BFS or DFS

24. Depth-limited search
Recursive implementation:
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25. Depth-Limited Search Complete? NO. Why? (l < d OR l > d)
Time? O(bl)
Space? O(bl)
Depth-first is a special case of depth-limited with l being infinite.
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26. Iterative deepening search
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27. Iterative deepening search l =0
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28. Iterative deepening search l =1
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29. Iterative deepening search l =2
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30. Iterative deepening search l =3
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31. Iterative Deepening search
Number of nodes generated in a depth-limited search to depth d with branching factor b:
NDLS = b0 + b1 + b2 + … + bd-2 + bd-1 + bd
Number of nodes generated in an iterative deepening search to depth d with branching factor b:
NIDS = (d+1)b0 + d b1 + (d-1)b2 + … + 3bd-2 +2bd-1 + 1bd
For b = 10, d = 5,
NDLS = , , ,000 = 111,111
NIDS = , , ,000 = 123,456
Overhead = (123, ,111)/111,111 = 11%
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32. Properties of iterative deepening search
Complete? Yes
Time? (d+1)b0 + d b1 + (d-1)b2 + … + bd = O(bd)
Space? O(bd)
Optimal? Yes, if step cost = 1
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33. Summary of Algorithms
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34. Questions
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