Bayesian Nets & Markov Blanket
In a Bayesian network, a variable is independent from all the variables given its Markov blanket (except of course the variables in the Markov blanket).

However, the Markov blanket is not the minimal set that renders two variables independent.

Also note that a variable may be independent of some variables in the Markov blanket, given another set of variables (think about the case of a spouse in the network).

By the way, I think that this problem has been solved already (if you refer to the problem of identifying the minimal set that renders two variables independent).

Edit: Check this out: http://www.cs.iastate.edu/~jtian/r254_min_separator.pdf
They show how to find a minimal d-separating set in a given Bayesian network.