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Slide 1 - Search Introduction toArtificial Intelligence COS302 Michael L. Littman Fall 2001
Slide 2 - Administration Short written homeworks each week First one today Web page is up with first lecture Send me (mlittman@cs) your email address so I can make a mailing list Office hours…
Slide 3 - What’s AI? (to me) Computers making decisions in real-world problems apply formulate solve
Slide 4 - Search Problems Let S be the set of states (strings) Input: Initial state: s0 Neighbor generator, N: S  2S Goal function, G: S  {0,1}
Slide 5 - Search Answer s1,…,sn such that: s1,…,sn  S for all 1in, si  N(si-1) G(sn) = 1
Slide 6 - Examples We’re very impressed. Meaning? Rush Hour 8-puzzle Logistics 8-queens problem Logic puzzles Job-shop scheduling
Slide 7 - Rush Hour Move cars forward and backward to “escape”
Slide 8 - Search Version States: configurations of cars N(s): reachable states G(s): 1 if red car at gate
Slide 9 - 8-puzzle Slide tiles into order States: N(s): G(s):
Slide 10 - Logistics Very sophisticated. What goes where when? Desert Storm logistics “paid for AI research”
Slide 11 - 8 Queens Puzzle No captures States: N(s): G(s):
Slide 12 - Logic Puzzles Jody, who is an ape, wasn’t the ape who returned immediately after Tom and immediately before the animal who appeared in the movie with no rating. The only lions that were used in the movies were the one who was the third to return, the one who appeared in the R movie, and the one who appeared in “Luck”. …
Slide 13 - Job-Shop Scheduling Industrial problem: Allocate machines and machinists to time slots Constraints on orders in which parts are serviced
Slide 14 - Search Template fringe = {(s0, 0)}; /* initial cost */ markvisited(s0); While (1) { If empty(fringe), return failure; (s, c) = removemincost(fringe); If G(s) return s; Foreach s’ in N(s) if unvisited(s’) fringe = fringe U {(s’, cost(s’)}; markvisited(s0); }
Slide 15 - Data Structures How implement this efficiently? removemincost-U-empty? markvisited-unvisited?
Slide 16 - Vary Cost How does search behavior change with cost? cost(s’) = c + 1 cost(s’) = c - 1
Slide 17 - Grid Example: BFS
Slide 18 - Grid Example: DFS
Slide 19 - How Evaluate? What makes one search scheme better than another? Completeness: Find solution? Time complexity: How long? Space complexity: Memory? Optimality: Find shortest path?
Slide 20 - Depth vs. Breadth-first Let |T(s)|  b (branching factor), goal at depth d How implement priority queue? Completeness? Time complexity? Space complexity? Optimality?
Slide 21 - BFS Completeness? Yes Time complexity? O(bd) Space complexity? O(bd)  Optimality? yes
Slide 22 - DFS Completeness? Yes, assuming state space finite Time complexity? O(|S |), can do well if lots of goals Space complexity? O(n), n deepest point of search Optimality? No 
Slide 23 - Depth-limited Search DFS, only expand nodes depth  l. Completeness? No, if l  d.  Time complexity? O(bl) Space complexity? O(l) Optimality? No 
Slide 24 - Iterative Deepening Depth limited, increasing l. Completeness? Yes.  Time complexity? O(bd), even with repeated work!  Space complexity? O(d)  Optimality? Yes 
Slide 25 - Bidirectional Search BFS in both directions Need N-1 How could this help? bl vs 2bl/2 What makes this hard to implement?
Slide 26 - Which do you choose? 8-queens, neighbors of s add one queen to board
Slide 27 - Which do you choose? Big grid, goal nearby
Slide 28 - What to Learn How to express problems in the search framework The basic algorithms for search Strengths and weaknesses of the basic algorithms
Slide 29 - Homework 1 (due 9/26) 1. Send your email address (right away) to littman@cs. 2. Let BFS’ and DFS’ be versions of BFS and DFS that don’t check whether a state has been previously visited. Evaluate BFS’ and DFS’ on the four comparison criteria we discussed. 3. Consider the Rush Hour board from these notes. Assume a single move consists of sliding a car forward or backward some number of spaces. (a) Give an upper bound on the branching factor. (b) Assuming the solution is at depth 20, how many nodes will be searched? (c) Ignoring the search, how many states are in the search space? Give as tight an upper bound as you can.