7_constraint_satisfaction_problems #5
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SepehrAsh
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Nov 5, 2021
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| Constraint Satisfaction | |||
| ============== | |||
| - [Constraint Satisfaction](#constraint-satisfaction) | |||
| - [Strong k-Consistency <div id='SKC'/>](#strong-k-consistency-div-idskc) | ||
| - [Using problem structure <div id='PS'/>](#using-problem-structure-div-idps) | ||
| - [Summary](#summary) | ||
| # Introduction |
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You Can Improve Your Introduction, Remember You Should Provide Information For Someone Who Is New To This Topic as well as informative ones.
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| ## N-Queens |
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| In cases which are almost tree form, there is a minimum cutset which includes a few members. In these cases, we can use *Conditioning method*. In this method, we first assign values to variables of the cutset in different ways. Then we solve the problem for other variables (which form a tree). If we consider $c$ as the size of the cutset, this method includes $d^c$ value assignments and then solving problem for the remaining tree which we know it has $O((n-c)d^2)$ time complexity. Hence, this method has $O(d^c.(n-c)d^2)$ time complexity which is good for small $c$. | ||
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| # Summary |
| - Tree-structured problems can be solved in linear time. | ||
| - Custset conditioning can make a general CSP structure to a tree-structured one. It is very efficient for small cutsets. | ||
| - Tree decomposition technique transform the CSP into a tree of subproblems. It is very efficient if tree width of the constraint graph is small. | ||
| - Time complexity of CSP is related to the structure of its constraint graph. |
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For example : Some articles that can be used for further reading, or extra details. Also, you can add your own references.
SepehrAsh
reviewed
Nov 5, 2021
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| In Constraint Satisfaction Problems, we are dealing with special form of search problems. These problems try to find some search algorithms that require new conditions. The conditions are Constraints. | ||
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| In CSPs, we have some variables $X_i$ that we should declare some values from domain $D_i$. |
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Pay attention to syntax ->
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used (https://render.githubusercontent.com) for rendering latex.
| # Examples | ||
| ## Map-Coloring | ||
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| For example: | ||
| $[WA : Red, NT : Green, SA : Blue, Q : Red, NSW : Green, V : Red, T : Green]$ | ||
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| - Tree-structured problems can be solved in linear time. | ||
| - Custset conditioning can make a general CSP structure to a tree-structured one. It is very efficient for small cutsets. | ||
| - Tree decomposition technique transform the CSP into a tree of subproblems. It is very efficient if tree width of the constraint graph is small. | ||
| - Time complexity of CSP is related to the structure of its constraint graph. |
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@sararajabzadeh @SepehrAsh