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Update AIMA - Chapter 6 - Constraint Satisfaction Problems.md
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AustinTSchaffer authored Apr 24, 2024
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- AI
- AIMA
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**# AIMA - Chapter 6 - Constraint Satisfaction Problems
# AIMA - Chapter 6 - Constraint Satisfaction Problems
- [[AIMA - Chapter 3 - Solving Problems by Searching]] and Chapter 4 (no chapter notes, module notes link: [[Module 02 - Simulated Annealing]])
- These prior chapters considered the "state" of a problem to be a black box, atomic, indivisible.
- Searching for solutions within the state space required domain-specific code to describe the transition between states.
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- **Conflict-directed backjumping** backtracks directly to the source of the problem.
- **Constraint learning** records the conflicts as they are encountered during search in order to avoid the same conflict later in the search.
- Local search using the **min-conflicts** heuristic has also been applied to constraint satisfaction problems with great success.
- The complexity of solving a CSP is strongly related to the structure of its constraint graph. Tree-structured problems can be solved in linear time. **Cutset conditioning** can reduce a general CSP to a tree-structured one and is quite efficient (requiring only linear memory) if a small cutset can be found. **Tree decomposition** techniques transform the CSP into a tree of subproblems and are efficient if the **tree width** of the constraint graph is small; however they need memory exponential in the tree width of the constraint graph. Combining cutset conditioning with tree decomposition can allow a better tradeoff of memory versus time.
- The complexity of solving a CSP is strongly related to the structure of its constraint graph. Tree-structured problems can be solved in linear time. **Cutset conditioning** can reduce a general CSP to a tree-structured one and is quite efficient (requiring only linear memory) if a small cutset can be found. **Tree decomposition** techniques transform the CSP into a tree of subproblems and are efficient if the **tree width** of the constraint graph is small; however they need memory exponential in the tree width of the constraint graph. Combining cutset conditioning with tree decomposition can allow a better tradeoff of memory versus time.

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