Note to "An efficient Data Structure for Lattice Operation"

This note is to publicly answer to a paper recently accepted to SWAT 2020 [1] that claims to have solved an error in our papers [3,2] by proposing a solution with worst performances. In the following section we describe in detail sections 4.2 (Cluster collection) and 5 (Data Structure and Space Complexity) in [3] to show the implementation of the data structure.