Sep 7, 2007
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- Formal algorithms for maintaining arc consistency
	- REVISE
	- AC1
	- AC3

- Arc consistency = 2-consistency

 What is 1-consistency by the way?
	- remove any violating variable from a domain

- Definitions
	- A graph is K-consistent if:
		- choose values for any (K-1) variables
	          (that satisfy constraints among them)
		- choose a Kth variable, then
		- there exists a value for this variable

- An n-node constraint graph
	- can be made n-consistent
		- in an aim to "read off" the answer
	- but sometimes, just k-consistent is enough
		- for k<n

- Interestingly,
	- as long as k is made > width of graph, then
	  you need no search/backtracking!
		- width is a "magic" number that has to be determined

- Thus, two ways to solve a CSP
	- solving a CSP using constraint propagation
		- can just 'read off' the answer
	- solving a CSP using search

- Third approach
	- "mix" CP and search
	- i.e., embed CP in a backtracking algorithm
		- at each node try to achieve *some* consistency
		- AND search