Lesson 09 - Module 4 Constraint satisfaction problems...

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Module 4 Constraint satisfaction problems Version 1 CSE IIT, Kharagpur
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4.1 Instructional Objective The students should understand the formulation of constraint satisfaction problems Given a problem description, the student should be able to formulate it in terms of a constraint satisfaction problem, in terms of constraint graphs. Students should be able to solve constraint satisfaction problems using various algorithms. The student should be familiar with the following algorithms, and should be able to code the algorithms o Backtracking o Forward checking o Constraint propagation o Arc consistency and path consistency o Variable and value ordering o Hill climbing The student should be able to understand and analyze the properties of these algorithms in terms of o time complexity o space complexity o termination o optimality Be able to apply these search techniques to a given problem whose description is provided. Students should have knowledge about the relation between CSP and SAT At the end of this lesson the student should be able to do the following: Formulate a problem description as a CSP Analyze a given problem and identify the most suitable search strategy for the problem. Given a problem, apply one of these strategies to find a solution for the problem. Version 1 CSE IIT, Kharagpur
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Lesson 9 Constraint satisfaction problems - I Version 1 CSE IIT, Kharagpur
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4.2 Constraint Satisfaction Problems Constraint satisfaction problems or CSP s are mathematical problems where one must find states or objects that satisfy a number of constraints or criteria. A constraint is a restriction of the feasible solutions in an optimization problem. Many problems can be stated as constraints satisfaction problems. Here are some examples: Example 1: The n-Queen problem is the problem of putting n chess queens on an n×n chessboard such that none of them is able to capture any other using the standard chess queen's moves. The colour of the queens is meaningless in this puzzle, and any queen is assumed to be able to attack any other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The problem was originally proposed in 1848 by the chess player Max Bazzel, and over the years, many mathematicians, including Gauss have worked on this puzzle. In 1874, S. Gunther proposed a method of finding solutions by using determinants, and J.W.L. Glaisher refined this approach. The eight queens puzzle has 92 distinct solutions. If solutions that differ only by symmetry operations (rotations and reflections) of the board are counted as one, the puzzle has 12 unique solutions. The following table gives the number of solutions for n queens, both unique and distinct. n : 6 7 8 9 10 11 12 13 14 15 unique: 1 0 0 1 2 1 6 12 46 92 341 1,787 9,233 45,752 285,053 1 0 0 2 10 4 40 92 352 724 2,680 14,200 73,712 Note that the 6 queens puzzle has, interestingly, fewer solutions than the 5 queens puzzle!
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This note was uploaded on 09/20/2010 for the course MCA DEPART 501 taught by Professor Hemant during the Fall '10 term at Institute of Computer Technology College.

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Lesson 09 - Module 4 Constraint satisfaction problems...

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