Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. In this book we provide comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND/OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. We believe the principles outlined here would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond.

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Rina Dechters research centers on computational aspects of automated reasoning and knowledge representation including search, constraint processing, and probabilistic reasoning. She is a Chancellors Professor of Computer Science at the University of California, Irvine. She holds a Ph.D. from UCLA, an M.S. degree in applied mathematics from the Weizmann Institute, anda B.S. in mathematics and statistics from the Hebrew University in Jerusalem. She is the author of Constraint Processing published by Morgan Kaufmann (2003), and of Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms published by Morgan and Claypool (2013). She has co-authored close to 200 research papers and has served on the editorial boards of:Artificial Intelligence, the Constraint Journal, Journal of Artificial Intelligence Research (JAIR), and Journal of Machine Learning Research (JMLR). She is a Fellow of the American Association of Artificial Intelligence since 1994, was a Radcliffe Fellow during 2005-2006, received the 2007 Association of Constraint Programming (ACP) Research Excellence Award, and became an ACM Fellow in 2013. She was a Co-Editor-in-Chief of Artificial Intelligence from 2011 to 2018 and is the conference chair-elect for IJCAI-2022.