CSE 473 Chapter 3 Problem Solving using Search · 2006. 10. 4. · 3 5 Example: N Queens 4 Queens 6 State-Space Search Problems General problem: Given a start state, find a path to
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Chapter 3
Problem Solving using Search
Chapter 3
Problem Solving using Search
CSE 473
© CSE AI Faculty
“First, they do an on-line search”
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Example: The 8-puzzleExample: The 8-puzzle
1 2 3
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1 2 3
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Example: Route PlanningExample: Route Planning
start
end
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Example: N QueensExample: N Queens
4 Queens
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Example: N QueensExample: N Queens
4 Queens
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State-Space Search ProblemsState-Space Search Problems
General problem:
Given a start state, find a path to a goal state
• Can test if a state is a goal
• Given a state, can generate its successor states
Variants:
• Find any path vs. a least-cost path
• Goal is completely specified, task is just to find the path
– Route planning
• Path doesn’t matter, only finding the goal state
– 8 puzzle
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Tree Representation of 8-Puzzle Problem SpaceTree Representation of 8-Puzzle Problem Space
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Space is the big problem for BFS.
Example: b = 10, 10,000 nodes/sec, 1KB/node
d = 2 ŁŁŁŁ 1100 nodes, 0.11 secs, 1MB
d = 4 ŁŁŁŁ 111,100 nodes, 11 secs, 106 MB
d = 8 ŁŁŁŁ 109 nodes, 31 hours, 1 TB
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Increasing path-cost limits instead of depth limits
This is called Iterative lengthening search (exercise 3.11)
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Forwards vs. BackwardsForwards vs. Backwardsstart
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Problem: Find the shortest route
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Bidirectional SearchBidirectional Search
Motivation: bd/2 + bd/2 << bd
Can use breadth-first search or uniform-cost search
Hard for implicit goals e.g., goal = “checkmate” in chess
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Repeated StatesRepeated States
Failure to detect repeated states can turn a linear problem into an exponential one! (e.g., repeated states in 8 puzzle)
Graph search algorithm: Store expanded nodes in a set called closed and only add new nodes to the fringe
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Graph SearchGraph Search
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Can we do better?Can we do better?
All these methods are slow (blind)
Solution àààà use problem-specific knowledge to guide search (“heuristic function”)
àààà “informed search” (next lecture)
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