For every cluster I ∈ C (τ ) we rec

For every cluster I ∈ C (τ ) we recall the standard notion
of parent (cluster) Pr (I, τ ) and lists of children Ch(I, τ )
of I in τ , illustrated in Figure 1. For the trivial case, we
set Pr (J, τ ) = ∅. Additionally, we find it useful to define
the local complement (sibling) of cluster I ∈ C (τ ) as
I−τ : = Pr (I, τ ) I, not to confused with the standard
(global) complement IC = J I. Further, a grandchild in τ
is a cluster G ∈ C (τ ) having a grandparent Pr2(G, τ ) : =
Pr