A complexity analysis of MPE inference in possibilistic networks

Reasoning with uncertainty in graphical models often implies great computational cost. For example, computing the most probable explanation in Bayesian networks is known to be NP
^PP
-complete. Possibilistic networks represent an alternative powerful representation for uncertain information. This paper aims at showing that the computation complexity of MPE inference tasks in possibilistic networks are NP-complete. To that end, we provide full reduction and proof for MPE querying min-based and product-based possibilistic networks. More precisely, we provide incremental proofs based on reductions to and from three well-known NP-complete problems: SAT, 3SAT and Weighted MaxSAT decision problems.