Regular Constraint - Pentomino Benchmark

[MaxOstrowski]

pentominos/05 seems just to post static regular constraints. No
variables involved ? (board isnt static)
Is this true ? Why do I use propagation... whats wrong there ...
Maybe not all values of board are set ?

[MaxOstrowski]

regular translates into quite some array_int_element constraints, which are again translated. Maybe look at this translation first!
Otherwise the a array could directly be created as boolean values, as numbers do not make much sense here.

[MaxOstrowski]

In the general case array_int_element (and as=array of integers) as[b]=c is translated to
as[1]*(b==1) + as[2]*(b==2) + ... + as[n]*(b==n) = c.
This introduces direct encoding variables for b, and equivalent {0,1} integer variables for them to be put into the constraint above.
A lot of equal variables are introduced, do not know how much overhead this makes.

[MaxOstrowski]

The array_var_int_element (and as=array of integer variables) as[b]=c constraint instead produces constraints of the form

b==1 -> c=as[1]
b==2 -> c=as[2]
...
b==n -> c=as[n]

This is more intuitive.
It does not introduce the equivalence {0,1} variables but much more smaller constraints.
I do not know which version has better propagation strength.

[MaxOstrowski]

A propagator for
&array_element(b){a(X),X : dom(X)} = c
could help reduce grounding a lot.

[MaxOstrowski]

In the case of array_int_element
as[1]*(b<=1) + as[2]*(b<=2) + ... + as[n]*(b<=n) = c
could be used if the array is ordered increasingly. (values in as would need to be adapted)

[MaxOstrowski]

For array_int_element a PB constraint could be used instead of a clingcon constraint, if c is a constant.
as[1]*(b==1) + as[2]*(b==2) + ... + as[n]*(b==n) = c
This saves a bit of grounding (equal variables) and could be a bit faster.

The same is true for the translation for cumulative.

Edit: Created a PB constraint for this to save a lille grounding and conversion from bool2int.