# Lect3 - Start reading Ch 7 8 9 Project topics Course web...

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1 Start reading Ch. 7, 8, 9 Project topics Course web site http://www.cs.illinois.edu/class/cs440/ or http://www.cs.uiuc.edu/class/fa10/cs440

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SEARCH(Problem P, Queuing Function QF): local: n /* current node */ q /* nodes to explore */ q singleton of Initial_State(P); Loop: if q = () return failure; n Pop(q); if n Solves P return n; q QF(q, Expand(n)); end Depth First: QF(old, new): Append(new, old); Breadth First: QF(old, new): Append(old, new); Generic Search Function 2
Sample Search Tree A D C B J I H G F E Depth First n q (between iterations) - (A) A (B C D) B (E F C D) E (F C D) F (C D) C (G D) G (D) 3

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Sample Search Tree A D C B J I H G F E Breadth First n q - (A) A (B C D) B (C D E F) C (D E F G) D (E F G H I J) E (F G H I J)    4
Costs Performing the search to find Goal Time Space Executing an operator in the world We will focus on execution cost We assume Positive finite cost for each action Finite branching factor Important cost functions: g, h, f 5

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Define: g*(n) as minimum cost from root to n n Nodes Define: g(n) as an easily computable approximation to g* How might we compute g? Need an execution cost model for each operator How might g(n) g*(n)? In fact it is usually easy to guarantee g(n) g*(n) (especially for trees!) Note the node alone determines which operators can apply next (First Order Markov: history is unimportant to world dynamics more later) 6
Define: h*(n) as minimum cost from n to a goal n Nodes Define: h(n) as an easily computable approximation to h* h is called a “heuristic function” Define: f(n) as g(n) + h(n) I n G g*(n) h*(n) Initial State Lowest cost solution constrained through n f(n) approximates this 7

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A search algorithm (together with its heuristic function if needed) is admissible iff for all search trees: A) If there exists a goal, the search will not fail.
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