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SP10 cs188 lecture 5 -- CSPs II (2PP)

SP10 cs188 lecture 5 -- CSPs II (2PP) - CS 188 Artificial...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 5: CSPs II 2/2/2010 Pieter Abbeel – UC Berkeley Many slides from Dan Klein 1 Announcements square4 Project 1 due Thursday square4 Lecture videos reminder: don’t count on it square4 Midterm square4 Section: CSPs square4 Tue 3-4pm, 285 Cory square4 Tue 4-5pm, 285 Cory square4 Wed 11-noon, 285 Cory square4 Wed noon-1pm, 285 Cory 2
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2 Today square4 CSPs square4 Efficient Solution of CSPs square4 Search square4 Constraint propagation square4 Local Search 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.: 5
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3 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! 6 Example: Cryptarithmetic square4 Variables (circles): square4 Domains: square4 Constraints (boxes): 7
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4 Example: Sudoku square4 Variables: square4 Each (open) square square4 Domains: square4 {1,2,…,9} square4 Constraints: 9-way alldiff for each row 9-way alldiff for each column 9-way alldiff for each region Example: The Waltz Algorithm square4 The Waltz algorithm is for interpreting line drawings of solid polyhedra square4 An early example of a computation posed as a CSP square4 Look at all intersections square4 Adjacent intersections impose constraints on each other ? 10
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5 Varieties of CSPs square4 Discrete Variables square4 Finite domains square4 Size d means O( d n ) complete assignments square4 E.g., Boolean CSPs, including Boolean satisfiability (NP-complete) square4 Infinite domains (integers, strings, etc.) square4 E.g., job scheduling, variables are start/end times for each job square4 Linear constraints solvable, nonlinear undecidable square4 Continuous variables square4 E.g., start-end state of a robot square4
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