MIT16_410F10_lec03

MIT16_410F10_lec03 - 1 Analysis of Uninformed Search...

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Unformatted text preview: 1 Analysis of Uninformed Search Methods Brian Williams, Fall 10 1 Brian C. Williams Draws from materials in: 16.410-13 6.034 Tomas Lozano Perez, Russell and Norvig AIMA Sep 15 th , 2010 6.046J Charles E. Leiserson Assignments • Assignment: – Problem Set #1 due today, Wed Sept 15 th , 2010. – Problem Set #2: Uninformed Search out today, due Wednesday, September 22 nd , 20010. • Reading: – Today: Asymptotic Analysis, Lecture 2 Notes of 6.046J Recurrences, Lecture 12 Notes of 6.042J. – Monday: Proofs & Induction, Lectures 2 and 3 of 6.042J. Brian Williams, Fall 10 2 Outline • Review • Analysis – Depth-first search – Breadth-first search • Iterative deepening Brian Williams, Fall 10 3 Autonomous Systems: • Plan complex sequences of actions • Schedule tight resources • Monitor and diagnose behavior • Repair or reconfigure hardware. formulate as state space search . Brian Williams, Fall 10 4 2 Formalizing Graph Search Input: A search problem SP = <g, S, G> where • graph g = <V, E>, • start vertex S in V, and • goal vertex G in V. Output: A simple path P = <S, v2, … G> in g from S to G . (i.e., <v i ,v i+1 > E, and v i v j if i j ). C S B G A D Brian Williams, Fall 10 5 Brian Williams, Fall 10 6 S B G A <S> <B, S> <A, S> <G, B, S> < A, B, S> Graph Search is a Kind of State Space Search S B A G B Graph Search is a Kind Of Tree Search 3 Solution: Depth First Search (DFS) S D B A C G C G D C G Solution: Breadth First Search (BFS) S D B A C G C G D C G Brian Williams, Fall 10 7 Brian Williams, Fall 10 8 S B G A <S> Generate (Q) Test <A, S> <B, S> Visited S 4 Pseudo Code For Simple Search Let g be a Graph G be the Goal vertex of g. S be the Start vertex of g Q be a list of simple partial paths in GR, 1. Initialize Q with partial path (S) as only entry; set Visited = ( ); 2. If Q is empty, fail. Else, pick some partial path N from Q; 3. If head(N) = G, return N; (goal reached!) 4. Else a) Remove N from Q; b) Find all children of head(N) (its neighbors in g) not in Visited and create a one-step extension of N to each child; c) Add to Q all the extended paths; d) Add children of head(N) to Visited; Brian Williams, Fall 10 9 e) Go to step 2. 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 A C C G D C B Breadth-first: Add path extensions to back of Q G Pick first element of Q G Brian Williams, Fall 10 10 5 Outline • Review • Analysis – Depth-first search – Breadth-first search • Iterative deepening Brian Williams, Fall 10 11 Elements of Algorithm Design Description: (last Monday) – Problem statement....
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This note was uploaded on 12/26/2011 for the course SCIENCE 16.410 taught by Professor Prof.brianwilliams during the Fall '10 term at MIT.

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MIT16_410F10_lec03 - 1 Analysis of Uninformed Search...

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