SP10 cs188 lecture 6 -- adversarial search (2PP)

SP10 cs188 lecture 6 -- adversarial search (2PP) - CS 188...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 6: Adversarial Search 2/4/2010 Pieter Abbeel – UC Berkeley Many slides adapted from Dan Klein 1 Announcements square4 Project 1 is due tonight square4 Written 2 is going out tonight, due next Thursday 2
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2 Today square4 Finish up Search and CSPs square4 Intermezzo on A* and heuristics square4 Start on Adversarial Search 3 CSPs: our status square4 So far: square4 CSPs are a special kind of search problem: square4 States defined by values of a fixed set of variables square4 Goal test defined by constraints on variable values square4 Backtracking = depth-first search with incremental constraint checks square4 Ordering: variable and value choice heuristics help significantly square4 Filtering: forward checking, arc consistency prevent assignments that guarantee later failure square4 Today: square4 Structure: Disconnected and tree-structured CSPs are efficient square4 Iterative improvement: min-conflicts is usually effective in practice 4
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3 Example: Map-Coloring square4 Variables: square4 Domain: square4 Constraints: adjacent regions must have different colors square4 Solutions are assignments satisfying all constraints, e.g.: 6 Constraint Graphs square4 Binary CSP: each constraint relates (at most) two variables square4 Binary constraint graph: nodes are variables, arcs show constraints square4 General-purpose CSP algorithms use the graph structure to speed up search. E.g., Tasmania is an independent subproblem! 7
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4 Tree-Structured CSPs square4 Theorem: if the constraint graph has no loops, the CSP can be solved in O(n d 2 ) time square4 Compare to general CSPs, where worst-case time is O(d n ) square4 This property also applies to probabilistic reasoning (later): an important example of the relation between syntactic restrictions and the complexity of reasoning. 8 Tree-Structured CSPs square4 Choose a variable as root, order variables from root to leaves such that every node’s parent precedes it in the ordering square4 For i = n : 2, apply RemoveInconsistent(Parent(X i ),X i ) square4 For i = 1 : n, assign X i consistently with Parent(X i ) square4 Runtime: O(n d 2 ) (why?) 9
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5 Tree-Structured CSPs square4 Why does this work?
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