Sep 08, 2003
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- a new type of search: constraint satisfaction search
        - map-coloring
        - cryptarithmetic problems
        - 4-queens

- (All) CSPs have
        - Variables
        - Domains
        - Constraints
                - can summarize in the form of
                  constraint graph

- Whats the big deal?
        - goal test is not a black box
        - goal test can be decomposed

- A really dumb algorithm for solving CSPs
        - Generate-and-test for 4-queens
        - is dumb because
                - order of assignment doesn't matter
                - once violated, nothing can unviolate a
                  constraint
                - doesn't use goal test effectively

- Better approach: backtracking
        - its really DFS
        - fixes some ordering and backtracks when
          constraints violated

- Problems with DFS
        - "thrashing"
        - search fails in different portions of
          the search space for the same reason

- More sophisticated viewpoint
	- MAC (maintaining arc consistency)
        - Defn: (V_i, V_j) is arc-consistent if for every
          value of V_i, there is an acceptable value of V_j

- Examples of constraint graphs
        - that are arc consistent, and 
        - that are not arc consistent

- MAC
        - remove violating values from domains
        - keep propagating (why?)
                - originally satisfied constraints might
                  suddenly get violated

- Arc consistency is sometimes useful
        - If all domains become 1, then you can
          "read off" the answer!
                - i.e., no backtracking in search
                  is needed

- In general
        - MAC might still require more search

- Complexity of MAC
        - O(ed^2) where
                - e: number of edges in graph
                - d: size of domain = |D|
	- your book uses n^2 instead of e
		- but its the same thing

- Different examples of constraint graphs and
  their relationship to MAC