<p>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. </p>

<p>Constraint propagation basically involves the concept of enforcing <strong>local consistency</strong> (this is done by enforcing node-consistency, arc-consistency, path-consistency and also global constraints using Alldiif or Atmost). </p>

<p>The terms: <strong>nodes</strong>, <strong>arc</strong>, <strong>path</strong>, 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 <strong>AC-3</strong>, <strong>PC-2</strong>, etc. precisely are for these purposes.</p>

CC BY-SA 4.0
2019-12-20T14:07:40.763Z
2019-12-20T14:07:40.763Z
MuneshSingh
<p>In the Constraint Propagation in CSP, it is often stated that <em>pre-processing</em> can solve the whole problem, so no search is required at all. And the key  idea is <strong>local consistency</strong>. What does this actually mean?</p>

CC BY-SA 4.0
2019-05-02T13:03:22.060Z
Have a look at [https://en.wikipedia.org/wiki/Local_consistency](https://en.wikipedia.org/wiki/Local_consistency).
nbro
CC BY-SA 4.0
2022-09-06T05:28:04.940Z
I think the consistency propagation method only works for 2-SAT problems, no?
PeaBrane
<terminology><definitions><constraint-satisfaction-problems>
What is local consistency in constraint satisfaction problems?
Lexi
# What is local consistency in constraint satisfaction problems?

(Asked by: username_0 on 2019-05-02)

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?

**Tags:** terminology, definitions, constraint-satisfaction-problems

> **Comments:**
> **username_1**: Have a look at [https://en.wikipedia.org/wiki/Local_consistency](https://en.wikipedia.org/wiki/Local_consistency).  
> **username_2**: I think the consistency propagation method only works for 2-SAT problems, no?  

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## 1 answers

### Answer by username_3 on 2019-12-20. Score: 0

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.


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