As Bayesian networks are applied to more complex and realistic real-world applications, the development of more efficient inference algorithms working under real-time constraints is becoming more and more important. This paper presents a survey of various exact and approximate Bayesian network inference algorithms. In particular, previous research on real-time inference is reviewed. It provides a framework for understanding these algorithms and the relationships between them. Some important issues in real-time Bayesian networks inference are also discussed.

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The algorithm selection problem aims at selecting the best algorithm for a given computational problem instance according to some characteristics of the instance. In this dissertation, we first introduce some results from theoretical investigation of the algorithm selection problem. We show, by Rice's theorem, the nonexistence of an automatic algorithm selection program based only on the description of the input instance and the competing algorithms. We also describe an abstract theoretical framework of instance hardness and algorithm performance based on Kolmogorov complexity to show that algorithm selection for search is also incomputable. Driven by the theoretical results, we propose a machine learning-based inductive approach using experimental algorithmic methods and machine learning techniques to solve the algorithm selection problem. Experimentally, we have