[2] give essentially the
same algorithm, but for the optimization problem of finding a minimization
of sums. In VE, we use the algorithm for finding the sum of
products. VE is named because of the links to the algorithm of
[2]; they refer to their basic algorithm as
The elimination of variables one by one, which is exactly what
we do. [2] also describe good elimination ordering
heuristics and refinements such as
eliminating variables in blocks and forms of conditioning which we
don't consider here.
The only difference between VE and BEBA is that BEBA requires an a
priori elimination ordering (and exploits the prior ordering for efficiency), whereas the VE allows for dynamic
selection of which variable to eliminate next.