Possibilistic Networks: MAP Query and Computational Analysis

Possibilistic networks are powerful graphical uncertainty representations based on possibility theory. This paper analyzes the computational complexity of querying min-based and product-based possibilistic networks. It particularly focuses on a very common kind of queries: computing maximum a posteriori explanation (MAP). The main result of the paper is to show that the decision problem of answering MAP queries in both min-based and product-based possibilistic networks is NP-complete. Such computational complexity results represent an advantage of possibilistic networks over probabilistic networks since MAP querying is NP
^PP
-complete in probabilistic Bayesian networks. We provide the proof based on reduction from the 3SAT decision problem to MAP querying possibilistic networks decision problem. As well as reductions that are useful for implementation of MAP queries using SAT solvers.