In Bayesian networks, a most probable explanation (MPE) is a most likely instantiation of all network variables given a piece of evidence. Solving (the decision version of) an MPE query is NP-hard. Recent work proposed a branch-and-bound search algorithm that finds exact solutions to MPE queries, where bounds are computed on a relaxed network obtained by a technique known as node splitting. In this work we study the impact of variable and value ordering on such a search algorithm. We study several heuristics based on the entropies of variables and on the notion of nogoods, and propose a new meta-heuristic that combines their strengths. Experiments indicate that search efficiency is significantly improved, allowing many hard problems to be solved for the first time.

Sajjad Ahmed Siddiqi, Jinbo Huang