Optimize algorithm

[YairSlobodin1]

4th and 5th bullets of #191

[YairSlobodin1]

Is this not doing exactly the job of ds.Product? I though all that's need is trying different associativity of ds.Product, and taking the smaller one. Each projection of a rule is a essentially a Set, just like Interval; it should be possible to extend each to a RuleSet, exactly like IntervalSet, and then the Product datatype should be amenable to support minimizing the number of partitions.

@elazarg we use ds.Product here. The additional code is necessary to handle all protocols and combinations with anyProtocol rules. Moreover, for a cross, we return two rules, whereas Partitions() returns three cubes.

The question is why, or rather, is it possible to generalize Product to accommodate for that. Any rule should be representable as a Set. The difference between rules and Sets is that rules are coarse-grained, that is, there are sets that cannot be described precisely using a single rule (they are not closed under union/subtraction). Generalizing the operations of Set to represent this should yield a Product that minimizes any collection of rules.

@elazarg After implementing both SG and nACL optimization, I don't currently see a strong case for generalizing them

[elazarg]

Is this not doing exactly the job of ds.Product? I though all that's need is trying different associativity of ds.Product, and taking the smaller one. Each projection of a rule is a essentially a Set, just like Interval; it should be possible to extend each to a RuleSet, exactly like IntervalSet, and then the Product datatype should be amenable to support minimizing the number of partitions.

@elazarg we use ds.Product here. The additional code is necessary to handle all protocols and combinations with anyProtocol rules. Moreover, for a cross, we return two rules, whereas Partitions() returns three cubes.

The question is why, or rather, is it possible to generalize Product to accommodate for that. Any rule should be representable as a Set. The difference between rules and Sets is that rules are coarse-grained, that is, there are sets that cannot be described precisely using a single rule (they are not closed under union/subtraction). Generalizing the operations of Set to represent this should yield a Product that minimizes any collection of rules.

@elazarg After implementing both SG and nACL optimization, I don't currently see a strong case for generalizing them

I see. The incentive for generalization is to make the models library more useful. The abstractions are not trivial though, so I think it's just a direction to keep in mind, to do it when opportunity arises.