It appears to be necessary to process these intersections too, though I don’t exactly understand why.
I have a fuzz test that implements Double and Triple LIMO, with the S_i sets calculated as “whatever remains of n static fuzz-derived topologically-valid sets”, on a fuzz-derived initial linearization for a fuzz-derived cluster, and then verifies:
- The resulting linearization is topological
- The resulting linearization’s diagram is at least as good as the initial one.
- The resulting feerate diagram at size \operatorname{size}(S_i) is at least \operatorname{fee}(S_i), for each i.
If I drop any of the 2^n-1 intersections, the test finds failures in the last condition.