"tuples with larger arity" is just computer scientist speak for "take more things into account".
Given the generality and popularity of sweepline algorithms in computational geometry, I'm wondering where the problem is here. Can't you just move a sweepline across a given territory in any direction and get a result? If you want maximum outrage (largest value of X in smallest area), I agree that's more complex and I'm not sure how you would prove an optimum result.
Given the generality and popularity of sweepline algorithms in computational geometry, I'm wondering where the problem is here. Can't you just move a sweepline across a given territory in any direction and get a result? If you want maximum outrage (largest value of X in smallest area), I agree that's more complex and I'm not sure how you would prove an optimum result.