Possibilistic graphical models are powerful modeling and reasoning tools for uncertain information based on possibility theory. In this paper, we provide an analysis of computational complexity of MAP and MPE queries for possibilistic networks. MAP queries stand for maximum a posteriori explanation while MPE ones stand for most plausible explanation. We show that the decision problems of answering MAP and MPE queries in both min-based and product-based possibilistic networks is NP-complete. Definitely, such results represent an advantage of possibilistic graphical models over probabilistic ones since MAP queries are NPPP -complete in Bayesian networks. Our proofs for querying min-based possibilistic networks make use of reductions from the 3SAT problem to querying possibilistic networks decision problem. Moreover, the provided reductions may be useful for the implementation of MAP and MPE inference engines based on the satisfiability problem solvers. As for product-based networks, the provided proofs are incremental and make use of reductions from SAT and its weighted variant WMAXSAT.

中文翻译：

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可能网络：MAP 和 MPE 推理的计算分析

可能性图模型是基于可能性理论的不确定信息的强大建模和推理工具。在本文中，我们对可能网络的 MAP 和 MPE 查询的计算复杂性进行了分析。MAP 查询代表最大的后验解释，而 MPE 查询代表最合理的解释。我们表明，在基于最小值和基于乘积的可能性网络中回答 MAP 和 MPE 查询的决策问题是 NP 完全的。当然，这样的结果代表了可能图形模型相对于概率图形模型的优势，因为 MAP 查询是 NP聚丙烯- 在贝叶斯网络中完成。我们查询基于 min 的可能网络的证明利用了从 3SAT 问题到查询可能网络决策问题的简化。此外，所提供的减少可能对基于可满足性问题求解器的 MAP 和 MPE 推理引擎的实现有用。至于基于产品的网络，提供的证明是增量的，并利用了 SAT 及其加权变体 WMAXSAT 的减少。