Methods, systems, and apparatus are provided to generate a most probable explanation (MPE) for a Bayesian Network (BN). A first data structure is populated by iterating from the leaves of a junction tree (derived from the BN) to the root and retaining maximum potentials along the way. A second data structure records selective index locations that map into the first data structure. These selective locations correspond to selective maximum potentials housed within the first data structure. All the selective maximum potentials are resolved once a root maximum potential is known for a given problem. The selective maximum potentials form a MPE through the junction tree to reach the result.