1. What to do when you don’t know anything know nothing
UnInformed Search
What to do when you don’t know anything know nothing

2. What to know Be able to execute (by hand) an algorithm for a problem
Know the general properties
Know the advantages/disadvantages
Know the pseudo-code
Believe you can code it

3. Assumptions of State-Space Model
Fixed number of operators
Finite number of operators
Known initial state
Known behavior of operators
Perfect Information
Real World  Micro World
What we can do.

4. Concerns State-space: tree vs graph?
Are states repeated?
Completeness: finds a solution if one exists
Time Complexity
Space Complexity: Major problem
Optimality: finds best solution
Assume Directed Acyclic graphs (DAGS)
no cycles
Later: adding knowledge

5. General Search Algorithm
Current State = initial state
While (Current State is not the Goal)
Expand State
compute all successors/ apply all operators
Store successors in Memory
Select a next State
Set Current state to next
If current state is goal: success, else failure

6. Derived Search Algorithms
Algorithm description incomplete
What is “store in memory”
What is “memory”
What is “select”
Different choices yield different methods.

7. Abstract tree for evaluation
Let T be a tree where each node has b descendants. B is the branching factor.
Suppose that a goal lies at depth d.
If goal is root, depth of solution is 0.
Unlike in theory, tree usually generated dynamically.

8. Breadth First Memory = Queue Store = add to end
Select = take from the front
Properties:
complete,
optimal: min of steps
Time/Space Complexity =
1+b+b^2…+b^d = [b^(d+1) -1 ]/ (b-1) = O(b^d)
Problem: Exponential memory Size.

9. Uniform Cost Now assume edges have positive cost
Storage = Priority Queue: scored by path cost
or sorted list with lowest values first
Select, add unchanged.
Complete & optimal
Time & space like Breadth.

10. Uniform Cost Example Root – A cost 1 Root – B cost 3 A -- C cost 4
B – C cost 1
C is goal state.
Why is Uniform cost optimal?
Expanded does not mean checked node.

11. Depth First Storage = Stack Add = push Select = Pop
Not complete (if infinite or cycles, otherwise complete)
Not optimal
Time: O(b^m), space O(bm) where m is max depth.

12. Depth Limited Depth First search with limit = l
Algorithm change: states not expanded if at depth k.
Complete : no
Time: O(b^k)
Space: O(b*l)
Complete if solution <=l, but not optimal.

13. Iterative Deepening Set l = 0 Repeat Until solution is found.
Do depth limited search to depth l
l = l+1
Until solution is found.
Complete & Optimal
Time: O(b^d)
Space: O(bd) when goal at depth d

14. Comparison Breadth vs ID
Branching Factor 10
Depth Breadth ID

15. Bidirectional Won’t work with most goal predicates
Needs identifiable goal states
Needs reversible operators.
Needs a good hashing functions to determine if states are the same.
Then: O(b^d/2) time if bf is b in both directions.

16. Bidirectional Search Simple Case:
Initial State = {Start State+ Goal State}
Operators:
forward from start, backwards from goal
Standard: Breadth in both directions
Check: newly generated states intersect fringe. (can be expensive)

17. Repeated States Occurs whenever reversible operators
Occurs in many problems
Improvements
Do not return to state on path
Do not return to k recent states
Do not return to any seen state
Memory costs increase for all algorithms

18. Grid World Start (0,0) Goal (8,8) Legal moves: up, down, left, right
What happens to algorithms?