l5_bw_uninf_sch2

l5_bw_uninf_sch2 - Analysis of Uninformed Search Methods...

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Analysis of Uninformed Search Methods Brian C. Williams Draws from materials in: 16.410-13 6.034 Tomas Lozano Perez, Russell and Norvig AIMA Se ssion 5 6.046J Charles E. Leiserson Brian Wil iams, Fal 05 1 Assignments Remember: Problem Set #2: Java and Search due Wednesday, September 26th, 2005. • Reading: – Uninformed search: more of AIMA Ch. 3 – Asymptotic analysis: lecture 2 notes 6.046J. Brian Wil iams, Fal 05 2 Outline • Review • Analysis – Depth-first search – Breadth-first search • Iterative deepening Brian Wil iams, Fal 05 3 Brian Wil iams, Fal 05 4 Complex missions must carefully: Most AI problems, like these, may be formulated as • Plan complex sequences of actions • Schedule tight resources • Monitor and diagnose behavior • Repair or reconfigure hardware. state space search. Courtesy of Kanna Rajan, NASA Ames. Used with permission. Brian Wil iams, Fal 05 5 Astronaut Goose Grain Fox Grain Fox Astronaut Goose Astronaut Grain Fox Goose Goose Astronaut Fox Grain Astronaut Goose Grain Fox Astronaut Goose Grain Fox Grain Astronaut Goose Fox Astronaut Goose Grain Fox Fox Astronaut Goose Grain Astronaut Goose Fox Grain Goose Fox Astronaut Grain Goose Grain Astronaut Fox Astronaut Grain Goose Fox Astronaut Fox Goose Grain Goose Grain Fox Astronaut Astronaut Goose Grain Fox • Generate Solution Problem Solving: Formulate Graph and Find Paths Formulate Goal Formulate Problem – States – Operators – Sequence of states Elements of Algorithm Design Description: (last Monday) – Problem statement, – Stylized pseudo code, sufficient to analyze and implement the algorithm, – Implementation (last Wednesday). Brian Wil iams, Fal 05 6 1
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The Problem of State Space Search Input : <Gr,S,G> where • State Space Gr is a (directed, unweighted) graph <V,E>, S ˛ V is a Start State, and G ˛ V is a Goal State. Output : A simple path P = <v 1 , v 2 …v n > from S to G • v 1 = S, v n = G, • <v ,v i+1 > ˛ E, and i • v i ? v j . Brian Wil iams, Fal 05 7 Issue: Starting at S and moving top to bottom, will depth-first search ever reach G? C S B G A D Brian Wil iams, Fal 05 9 How Do We Avoid Repeat Visits? Idea: Keep track of vertices already visited. Do not place visited vertices on Q. Does this maintain correctness? Any goal reachable from a vertex that was visited a second time would be reachable from that vertex the first time. Does it always improve efficiency? Visits only a subset of the original paths (simple ones), such that each vertex appears at most once at the head of a path in Q . Brian Wil iams, Fal 05 11 Solution: Depth First Search (DFS) S D B A C G C G D C G Depth-first: Add path extensions to front of Q Pick first element of Q Solution: Breadth First Search (BFS) S D B A C G C G D C G Breadth-first: Add path extensions to back of Q Pick first element of Q Brian Wil iams, Fal 05 8 Depth-First Effort can be wasted in more mild cases Q 1 (S) 2 (A S) (B S) 3 (C A S) (D A S) (B S)
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l5_bw_uninf_sch2 - Analysis of Uninformed Search Methods...

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