UnInformed Search

1
UnInformed Search

• What to do when you dont know anything

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
Depth First

• Storage Stack
• Add push
• Select Pop
• Not complete (if infinite or cycles, otherwise
  complete)
• Not optimal
• Time O(bm), space O(bm) where m is max depth.

9
Ex. DFS for Permutations of 3

• Initial State lt-gt
• Next State add to front, no repeats
• Stack lt-gt
• Next Stack lt1gt,lt2gt,lt3gt
• Next Stack lt lt1,2gt, lt1,3gt, lt2gt, lt3gt etc
• Trick encode states with legal operators
• lt-gt ? lt-,1,2,3gt
• How much memory? O(n2)

10
Breadth First

• Memory Queue
• Store add to end
• Select take from the front
• Properties
• complete,
• optimal min of steps
• Time/Space Complexity
• 1bb2bd b(d1) -1 / (b-1) O(bd)
• Problem Exponential memory Size.

11
Ex. BFS for Permutations of 3

• Init lt-gt
• Queue lt-gt
• Next Queue lt1gt, lt2gt, lt3gt
• Next Queue lt2gt,lt3gt, lt1,2gt, lt1,3gt
• So whats the big deal?
• Space n!n for n! search.

12
Uniform Cost

• Now assume edges have positive cost
• Storage Priority Queue scored by path cost
• or sorted list with lowest values first
• Select- choose minimum cost
• add maintains order
• Check careful only check minimum cost for goal
• Complete optimal
• Time space like Breadth.

13
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.

14
Watch the queue

• R/0 // Path/path-cost
• R-A/1, R-B/3
• R-B/3, R-A-C/5
• Note you dont test expanded node
• You put it in the queue
• R-B-C/4, R-A-C/5

15
Depth Limited

• Depth First search with limit l
• Algorithm change states not expanded if at depth
  k.
• Complete no
• Time O(bk)
• Space O(bl)
• Complete if solution ltl, but not optimal.

16
Iterative Deepening

• Set l 0
• Repeat
• Do depth limited search to depth l
• l l1
• Until solution is found.
• Complete Optimal
• Time O(bd)
• Space O(bd) when goal at depth d

17
Comparison Breadth vs ID

• Branching Factor 10
• Depth Breadth ID
• 0 1 1
• 1 11 12
• 2 111
  123
• 3 1111
  1234
• 4 11111 12345

18
Bidirectional

• Wont 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(bd/2) time if bf is b in both
  directions.

19
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)

20
Repeated States

• Occurs whenever reversible operators
• Occurs in many problems
• Improvements
• Do not return to k recent states
• cheap and non-effective
• Do not return to state on path
• cycle checking Cheap and effective
• Do not return to any seen state exponential
• Memory costs increase for all algorithms

21
Algorithm Effects

• Cycles
• DFS incomplete fix cycle checking
• IDS incomplete fix cycle checking
• BFS still complete, but increased cost

22
Grid World

• Start (0,0)
• Goal (8,8)
• Legal moves up, down, left, right
• What happens to algorithms?