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Suppose, we are given a dominance constraint and one of its solutions. With each node of the constraint graph N
(i.e. each of its variables), we associate 4 mutually exclusive 4 finite sets of nodes:
N.eq
, the set of graph nodes of whose interpretation is equal N
,
N.up
, the set of graph nodes whose interpretations are strictly above N
,
N.down
, the set of graph nodes whose interpretations are strictly below N
,
N.side
, the set of graph nodes whose interpretations are to the side of N
.
The whole idea of our approach resides here: we encode a dominance constraints into set constraints such that each node in the constraint graph is modelled by the 4 set variables that we constrain to the sets above (in each solution).
The first constraint we require is the following: For all nodes N
, the 4 sets for N
are disjoint and form a partition of the set V of all nodes of the constraint graph:
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