Add DisjointCover node

[smharwood]

Adds a logical-valued node that determines whether its predecessors are a disjoint cover of a given primary set

Reference issue

What does this implement/fix?

Implements a DisjointCover node, enabling construction of DisjointLists via List symbols

AI Generation Disclosure

No AI tools used

[arcondello]

Couple random aesthetic comments

[arcondello]

Misc unhelpful notes from trying to find precedent for similar functions in other libraries we like to follow.

• NumPy's Set routines. Much closer to Consider adding Intersection and Union nodes/symbols #45 than this.
• Python's set methods. One thing to learn there is I think we want IsDisjointCover if we're outputting a bool? Definitely if we were implementing a Disjoint symbol we'd want IsDisjoint. In this case it's not clear what DisjointCover would be, so maybe adding Is* is redundant?

Maybe we want IsPartition? Though I am a little nervous about clashing with np.partition() which is a totally different thing. And I think a partition might actually requires that each subset be non-empty.

[arcondello]

I think if we were writing this from scratch we'd want an API like

from dwave.optimization import Model, is_disjoint_cover

model = Model()

universe = 100
num_lists = 10

lists = [model.list(universe, min_size=0) for _ in range(num_lists)]

model.add_constraint(is_disjoint_cover(lists))

open to suggestions

[smharwood]

Misc unhelpful notes from trying to find precedent for similar functions in other libraries we like to follow.

• NumPy's Set routines. Much closer to Consider adding Intersection and Union nodes/symbols #45 than this.
• Python's set methods. One thing to learn there is I think we want IsDisjointCover if we're outputting a bool? Definitely if we were implementing a Disjoint symbol we'd want IsDisjoint. In this case it's not clear what DisjointCover would be, so maybe adding Is* is redundant?

Maybe we want IsPartition? Though I am a little nervous about clashing with np.partition() which is a totally different thing. And I think a partition might actually requires that each subset be non-empty.

I'm convinced adding "Is" is the way to go. At least, its consistent with "IsIn", and its probably not a good idea to go the other way and rename that to just "In"

[smharwood]

I think if we were writing this from scratch we'd want an API like

from dwave.optimization import Model, is_disjoint_cover

model = Model()

universe = 100
num_lists = 10

lists = [model.list(universe, min_size=0) for _ in range(num_lists)]

model.add_constraint(is_disjoint_cover(lists))

open to suggestions

So, add is_disjoint_cover to the mathematical namespace?

[smharwood]

Can't tell if I should future-proof this interface and make the primary set an ArraySymbol? (but for now, just assert its a constant)

[smharwood]

I think if we were writing this from scratch we'd want an API like

from dwave.optimization import Model, is_disjoint_cover

model = Model()

universe = 100
num_lists = 10

lists = [model.list(universe, min_size=0) for _ in range(num_lists)]

model.add_constraint(is_disjoint_cover(lists))

open to suggestions

Finally revisiting this and I think I understand your suggestion: you would prefer to remove the "primary set size" argument to is_disjoint_cover and just infer it from the (common) max value of the lists?

I'm tempted to agree - this would address my other comment about future-proofing the interface. Just wondering if we wouldn't want the flexibility in the future.

[arcondello]

Can make it a kwarg with primary_set_size=None where None means infer from inputs?