Greedy search-based structure learning algorithm for Bayesian Network

It is a score-based search algorithm to learn the structure of BN. Steps are described as below:

1. Select an initial DAG G0, from which to start the search;
2. Calculate Bayes factors between D0 and all possible networks, which differ by only one arrow, that is:
(1) One arrow is added to D0;
(2) One arrow in D0 is deleted;
(3) One arrow in D0 is turned.
3. Among all these networks, select the one that increases the Bayes factor the most;
4. If the Bayes factor is not increased, stop the search. Otherwise, let the chosen network be D0 and repeat from 2.

This algorithm is borrowed from Heckman et al's, and it is customized to DEAL, a BN package on R.