SP11 cs188 lecture 5 -- CSPs II 6PP

SP11 cs188 lecture 5 -- CSPs II 6PP - A*: Robotics Examples...

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1 CS 188: Artificial Intelligence Spring 2011 Lecture 5: CSPs II 2/2/2011 Pieter Abbeel – UC Berkeley Many slides from Dan Klein 1 A*: Robotics Examples s Urban Challenge s Successor function? s Heuristic? s Door Opening s Successor function? s Heuristic? Other A* Applications s Pathing / routing problems s Resource planning problems s Robot motion planning s Language analysis s Machine translation s Speech recognition s Announcements s Project 1 due Friday 4:59pm s See course website for this week’s office hours, held by P1 GSI s Lecture videos online s Written Assignment Policy 4 Today s CSPs s Efficient Solution of CSPs s Search s Constraint propagation s Local Search 5 Constraint Satisfaction Problems s Standard search problems: s State is a “black box”: arbitrary data structure s Goal test: any function over states s Successor function can be anything s Constraint satisfaction problems (CSPs): s A special subset of search problems s State is defined by variables X i with values from a domain D (sometimes D depends on i ) s Goal test is a set of constraints specifying allowable combinations of values for subsets of variables s Simple example of a formal representation language s Allows useful general-purpose algorithms with more power than standard search algorithms 6
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2 Example CSP: Map-Coloring s Variables: s Domain: s Constraints: adjacent regions must have different colors s Solutions are assignments satisfying all constraints, e.g.: 7 Example CSP: N-Queens s Formulation 1: s Variables: s Domains: s Constraints 8 Example CSP: N-Queens s Formulation 2: s Variables: s Domains: s Constraints: Implicit: Explicit: -or- 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! 12 Example CSP: Cryptarithmetic s Variables (circles): s Domains: s Constraints (boxes): 14 Example CSP: 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
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3 Example CSP: The Waltz Algorithm s The Waltz algorithm is for interpreting line drawings of
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SP11 cs188 lecture 5 -- CSPs II 6PP - A*: Robotics Examples...

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