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This paper identifies and solves a new optimization problem: Given a beliefnetwork (BN) and a target ordering on its variables, how can we efficientlyderive its minimal I-map whose arcs are consistent with the target ordering? Wepresent three solutions to this problem, all of which lead to directed acyclicgraphs based on the original BN's recursive basis relative to the specifiedordering (such a DAG is sometimes termed the boundary DAG drawn from the givenBN relative to the said ordering [5]). Along the way, we also uncover animportant general principal about arc reversals: when reordering a BN accordingto some target ordering, (while attempting to minimize the number of arcsgenerated), the sequence of arc reversals should follow the topologicalordering induced by the original belief network's arcs to as great an extent aspossible. These results promise to have a significant impact on the derivationof consensus models, as well as on other algorithms that require thereconfiguration and/or combination of BN's.

Deriving a Minimal I-map of a Belief Network Relative to a Target Ordering of its Nodes