Systematic vs. Non-systematic Algorithms for Solving the MPE Task

The paper explores the power of two system­ atic Branch and Bound search algorithms that exploit partition-based heuristics, BBBT (a new algorithm for which the heuristic information is constructed during search and allows dy­ namic variable/value ordering) and its predeces­ sor BBMB (for which the heuristic information is pre-compiled) and compares them against a number of popular local search algorithms for the MPE problem as well as against the recently pop­ ular iterative belief propagation algorithms. We show empirically that the new Branch and Bound algorithm, BBBT demonstrates tremendous prun­ ing of the search space far beyond its predecessor, BBMB which translates to impressive time sav­ ing for some classes of problems. Second, when viewed as approximation schemes, BBBT/BBMB together are highly competitive with the best known SLS algorithms and are superior, espe­ cially when the domain sizes increase beyond 2. The results also show that the class of belief prop­ agation algorithms can outperform SLS, but they are quite inferior to BBMBIBBBT. As far as we know, BBBT/BBMB are currently among the best performing algorithms for solving the MPE task.