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 s Project 1 due Thursday s Lecture videos reminder: don’t count on it s Midterm s Section: CSPs s Tue 3-4pm, 285 Cory s Tue 4-5pm, 285 Cory s Wed 11-noon, 285 Cory s Wed noon-1pm, 285 Cory 2
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2 Today s CSPs s Efficient Solution of CSPs s Search s Constraint propagation s Local Search 3 Example: Map-Coloring s Variables: s Domain: s Constraints: adjacent regions must have different colors s Solutions are assignments satisfying all constraints, e.g.: 5
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3 Constraint Graphs s Binary CSP: each constraint relates (at most) two variables s Binary constraint graph: nodes are variables, arcs show constraints s General-purpose CSP algorithms use the graph structure to speed up search. E.g., Tasmania is an independent subproblem! 6 Example: Cryptarithmetic s Variables (circles): s Domains: s Constraints (boxes): 7
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4 Example: Sudoku s Variables: s Each (open) square s Domains: s {1,2,…,9} s Constraints: 9-way alldiff for each row 9-way alldiff for each column 9-way alldiff for each region Example: The Waltz Algorithm s The Waltz algorithm is for interpreting line drawings of solid polyhedra s An early example of a computation posed as a CSP s Look at all intersections s Adjacent intersections impose constraints on each other ? 10
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5 Varieties of CSPs s Discrete Variables s Finite domains s Size d means O( d n ) complete assignments s E.g., Boolean CSPs, including Boolean satisfiability (NP-complete) s Infinite domains (integers, strings, etc.) s E.g., job scheduling, variables are start/end times for each job s Linear constraints solvable, nonlinear undecidable s Continuous variables s E.g., start-end state of a robot s Linear constraints solvable in polynomial time by LP methods
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SP10 cs188 lecture 5 -- CSPs II (2PP) - CS 188 Artificial...

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