  This paper identifies and solves a new optimization problem: Given a belief
network (BN) and a target ordering on its variables, how can we efficiently
derive its minimal I-map whose arcs are consistent with the target ordering? We
present three solutions to this problem, all of which lead to directed acyclic
graphs based on the original BN's recursive basis relative to the specified
ordering (such a DAG is sometimes termed the boundary DAG drawn from the given
BN relative to the said ordering [5]). Along the way, we also uncover an
important general principal about arc reversals: when reordering a BN according
to some target ordering, (while attempting to minimize the number of arcs
generated), the sequence of arc reversals should follow the topological
ordering induced by the original belief network's arcs to as great an extent as
possible. These results promise to have a significant impact on the derivation
of consensus models, as well as on other algorithms that require the
reconfiguration and/or combination of BN's.
