[gecode-users] Operation of precede constraint on array of sets

[Tim Potter]

Hi everyone.  I hope this isn't some silly misunderstanding but I'm having trouble figuring out how the precede() constraint works when applied to SetVarArray.

Imagine I have a set of tasks with dependencies, for example 1->2, 2->3 and 3->4 to keep things simple.  I've added the following constraints:

    // Array of sets of integers from {1..4}

    SetVarArray deps(*this, 4, IntSet::empty, IntSet(1, 4));

    // Enforce pairwise disjointedness

    sequence(*this, deps);

    // Final task must appear

    rel(*this, setunion(deps) >= IntSet(IntArgs(1, 4)));

    // Task ordering constraints

    precede(*this, deps, 1, 2);
    precede(*this, deps, 2, 3);
    precede(*this, deps, 3, 4);

Now this should produce at least a solution like {{1}, {2}, {3}, {4}}.  However I get this as my first solution in the output:

	{{1..4}, {}, {}, {}}

which indicates that the precede() constraint is not behaving as I think it should.  

According to to the documentation the precede(home, x, s, t) version of the value precedence constraint as applied to set variables says that s is not an element of x_j and t is an element of x_j, then i < j such that s is an element of x_i and t is not an element of x_i. 

I don't understand how the solution above satisfies the above unless maybe the i < j is really acting as i <= j.  This seems to be the case based on the other solutions as they're sorted but that could be a side effect of the sequence() constraint.

Does anyone know what I'm doing wrong here?


Thanks,

Tim.