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Uninformed Search (2)

Lecture 5Introduction to Artificial Intelligence

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Introduction to Artificial IntelligenceHadi Moradi

moradi@usc.edu

Review: BFSCompleteness:Completeness:

Yes, Time complexity:

O(b d), Space complexity:

O(b d), Optimality:

SS

AA DD

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Optimality:Yes b – max branching factor d – depth of the least-cost solutionm – max depth

BB DD AA EE

CC EE EE BB BB FF

DD FF BB FF CC EE AA CC GG

GGGGGG FFCC

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Review: Uniform Cost

Completeness: SSYes,

Time complexity:O(b d),

Space complexity:O(b d),

Optimality:

SS

AA DD

BB DD AA EE

EE BB BB FF

33 44

44 55

55

55 22

55 44

33 44

77 88 99 66

10101111CC EE

44 551111 1212 1313 1313

44

3

Optimality:Yes BB FF CC EE AA CC GG

GGGG FFCC

33DD FF

GG

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Review: DFSCompleteness: YesCompleteness: Yes, Time complexity: O(b m), Space complexity:O(bm), Optimality: No

b – max branching factor d – depth of the least-cost solution

BB

SS

AA

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solutionm – max depth CC EE

DD FF

GG

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Depth First Search

Problem: Not remembering the previousProblem: Not remembering the previous states

Time complexity

Solution:Combine the depth first search and breath first

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psearch

Depth-limited search

It i d th fi t h ith d th li itIt is a depth-first search with depth limit

Implementation: Nodes at depth l have no successors.

Complete:

Optimal:

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p

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Iterative deepening searchFunction Iterative-deepening-Search(problem) returns a solution, or failurep g (p ) ,

for depth = 0 to ∞ doresult Depth-Limited-Search(problem, depth)if result succeeds then return result

endreturn failure

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Combines the best of breadth-first and depth-first search strategies.• Completeness: • Time complexity:• Space complexity:• Optimality:

Romania with step costs in km

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Iterative deepening complexity

Iterative deepening search may seem wastefulIterative deepening search may seem wasteful because so many states are expanded multiple times.

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Bidirectional search

Both search forward from initial stateBoth search forward from initial state, and backwards from goal.Stop when the two searches meet in the middle.

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GoalGoalStartStart

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Bidirectional search

1 QUEUE1 <1 QUEUE1 < path only containing the root;path only containing the root;1. QUEUE1 <1. QUEUE1 <---- path only containing the root;path only containing the root;QUEUE2 <QUEUE2 <---- path only containing the goal;path only containing the goal;

2. 2. WHILEWHILE both QUEUEs are not emptyboth QUEUEs are not emptyANDAND QUEUE1 and QUEUE2 do NOT share a stateQUEUE1 and QUEUE2 do NOT share a state

DODO remove their first paths;remove their first paths;create their new paths (to all children);create their new paths (to all children);

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p ( );p ( );reject their new paths with loops;reject their new paths with loops;add their new paths to back;add their new paths to back;

3. 3. IFIF QUEUE1 and QUEUE2 share a stateQUEUE1 and QUEUE2 share a stateTHENTHEN success;success;ELSEELSE failure;failure;

Bidirectional search• Completeness:• Completeness: • Time complexity:• Space complexity:• Optimality:

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Bidirectional search

Bidirectional search meritsBidirectional search meritsBig difference for problems with branching factor b in both directions

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Bidirectional searchBidirectional search issues

Predecessors of a node need to be generated

What to do if there is no explicit list of goalstates?

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What is the best search strategy for the two searches?

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Comparing uninformed search strategies

Criterion Breadth Uniform DepthFirst DepthLim Iterative Bidirectional

Time b^d b^d b^m b^l b^d b^(d/2)

Space b^d b^d bm bl bd b^(d/2)

Optimal? Yes Yes No No Yes Yes

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Complete? Yes Yes No Yes if l≥d Yes Yesb – max branching factor of the search treed – depth of the least-cost solutionm – max depth of the state-space (may be infinity)l – depth cutoff

Summary

Problem formulation usually requiresProblem formulation usually requires abstracting away real-world details to define a state space that can be explored using computer algorithms.

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Once problem is formulated in abstract form, complexity analysis helps us picking out best algorithm to solve problem.

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Summary

Variety of uninformed search strategies;Variety of uninformed search strategies; difference lies in method used to pick node that will be further expanded.

Iterative deepening search only uses

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Iterative deepening search only uses linear space and not much more time than other uniformed search strategies.