In the Constraint Propagation in CSP, it is often stated that pre-processing can solve the whole problem, so no search is required at all. And the key idea is local consistency. What does this actually mean?
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1$\begingroup$ Have a look at https://en.wikipedia.org/wiki/Local_consistency. $\endgroup$– nbroCommented May 2, 2019 at 13:03
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$\begingroup$ I think the consistency propagation method only works for 2-SAT problems, no? $\endgroup$– PeaBraneCommented Sep 6, 2022 at 5:28
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1 Answer
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If we can do some reduction in the search space using CSP (constraint propagation) we can drastically reduce the search space or sometimes completely avoid the need for a search by directly reaching the solutions (for e.g. with variables having their domains reduced to size one). It could also happen that we come to a point when a variable domain size becomes zero, in that case no solution exists, given the constraints, so no need for a search.
Constraint propagation basically involves the concept of enforcing local consistency (this is done by enforcing node-consistency, arc-consistency, path-consistency and also global constraints using Alldiif or Atmost).
The terms: nodes, arc, path, etc. basically reflects a CSP problem represented as a graph with nodes as the variables and the arcs/edges as constraints. The process is simply to remove values from the domains of the variables that are inconsistent. Algorithms such as AC-3, PC-2, etc. precisely are for these purposes.
