# m5-csp - Problems Chapter5 Section13 4Feb2004 1 Outline...

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4 Feb 2004 CS 3243 - Constraint Satisfaction 1 Constraint Satisfaction  Problems Chapter 5 Section 1 – 3

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4 Feb 2004 CS 3243 - Constraint Satisfaction 2 Outline Constraint Satisfaction Problems (CSP) Backtracking search for CSPs Local search for CSPs
4 Feb 2004 CS 3243 - Constraint Satisfaction 3 Constraint satisfaction problems (CSPs) Standard search problem: state  is a "black box“ – any data structure that supports successor  function, heuristic function, and goal test CSP: state  is defined by  variables   X i  with  values  from  domain   D i goal test  is a set of  constraints  specifying allowable combinations of  values for subsets of variables Simple example of a  formal representation language Allows useful  general-purpose  algorithms with more power  than standard search algorithms

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4 Feb 2004 CS 3243 - Constraint Satisfaction 4 Example: Map-Coloring Variables   WA, NT, Q, NSW, V, SA, T   Domains   D i  = {red,green,blue} Constraints : adjacent regions must have different colors e.g., WA ≠ NT, or (WA,NT) in {(red,green),(red,blue),(green,red),  (green,blue),(blue,red),(blue,green)}
4 Feb 2004 CS 3243 - Constraint Satisfaction 5 Example: Map-Coloring Solutions  are  complete  and  consistent   assignments, e.g., WA = red, NT = green,Q =  red,NSW = green,V = red,SA = blue,T = green

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4 Feb 2004 CS 3243 - Constraint Satisfaction 6 Constraint graph Binary CSP:  each constraint relates two variables Constraint graph:  nodes are variables, arcs are constraints
4 Feb 2004 CS 3243 - Constraint Satisfaction 7 Varieties of CSPs Discrete variables finite domains: n  variables, domain size   O(d n complete assignments e.g., Boolean CSPs, incl.~Boolean satisfiability (NP-complete) infinite domains: integers, strings, etc. e.g., job scheduling, variables are start/end days for each job need a constraint language, e.g.,  StartJob 1  + 5 ≤ StartJob 3 Continuous variables e.g., start/end times for Hubble Space Telescope observations linear constraints solvable in polynomial time by linear programming

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4 Feb 2004 CS 3243 - Constraint Satisfaction 8 Varieties of constraints Unary  constraints involve a single variable,  e.g., SA ≠ green Binary  constraints involve pairs of variables,
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## This note was uploaded on 10/22/2011 for the course CS CS 2710 taught by Professor Wiebe during the Fall '11 term at Pittsburgh.

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m5-csp - Problems Chapter5 Section13 4Feb2004 1 Outline...

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