This document discusses constraint satisfaction problems (CSP) and the CSP solving technique called forward checking. It provides an example of a map coloring CSP problem and then explains forward checking, which tracks remaining legal values for unassigned variables and terminates the search when a variable has no legal values left. It also discusses using heuristics like the degree heuristic, minimum remaining values heuristic, and least constraining value heuristic to guide the search order during forward checking.

1. CSP-Forward Checking
Presented by ,
Sourav Kairy
ID:171-115-128
Md. Juwel Ahmad
ID:171-115-152

2. Constraint satisfaction problems
● An assignment is complete when every value is mentioned.
● A solution to a CSP is a complete assignment that satisfies all
constraints.
● Applications: Scheduling the time of observations on the Hubble
Space Telescope, Floor planning, Map coloring, Cryptography

3. CSP example:Map-Coloring
● Variables WA, NT, Q, NSW, V, SA, T
● Domains Di = {red,green,blue}
● Constraints: adjacent regions must have
different colors
● e.g., WA ≠ NT, or (WA,NT) in
{(red,green),(red,blue),(green,red),
(green,blue),(blue,red),(blue,green)}

4. Goal
Solutions are complete and
consistent assignments, e.g.,
WA = red,
NT = green,
Q = red,
NSW = green,
V = red,
SA = blue,
T = green

5. Introduction
● Constraints between the current variable and the future
variables.
● That it detects also the conflicts between future variables and
therefore allows branches of the search tree.
● Forward checking is a type of filtering used in backtracking
search.
● Useful for detecting inevitable failures early.
Forward checking:

6. Degree heuristic
● Use degree heuristic
● Rule: select variable that is involved in the largest number of
constraints on other unassigned variables.
● Degree heuristic is very useful as a tie breaker.
● In what order should its values be tried?

7. Minimum remaining values(variable ordering)
● A.k.a. most constrained variable heuristic.
● Rule: choose variable with the fewest legal moves .
● Which variable shall we try first?

8. Least constraining domain value(value ordering)
Remaining 1 value for SA
Remaining 0 value for SA
● Least constraining value heuristic.
● Rule: given a variable choose the least constraining
value i.e. the one that leaves the maximum flexibility
for subsequent variable assignments.

9. Forward Checking Example
•Idea:
–Keep track of remaining legal values for unassigned
variables
–Terminate search when any variable has no legal
values

10. Forward Checking
WA NT SA Q NSW V T

11. Forward Checking
WA NT SA Q NSW V T

12. Forward Checking
WA NT SA Q NSW V T

13. Forward Checking
WA NT SA Q NSW V T

14. WA NT SA Q NSW V T
Forward Checking

15. WA NT SA Q NSW V T
Forward Checking

16. WA NT SA Q NSW V T
Forward Checking

17. Advantages
Forward checking allows us to see when problems arise as
we assign a new variable and to exit early to avoid doing
unnecessary work
Disadvantages
Forward checking does not provide early detection for all
failures. Particularly, it does not detect failures between two
unassigned variables.