Message Passing Algorithms (original) (raw)
Constraint Satisfaction Problems (CSPs) are defined over a set of variables whose state must satisfy a number of constraints. We study a class of algorithms called Message Passing Algorithms, which aim at finding the probability distribution of the variables over the space of satisfying assignments. These algorithms involve passing local messages (according to some message update rules) over the edges of a factor graph constructed corresponding to the CSP. We focus on the Belief Propagation (BP) algorithm, which finds exact solution marginals for tree-like factor graphs. However, convergence and exactness cannot be guaranteed for a general factor graph. We propose a method for improving BP to account for cycles in the factor graph. We also study another message passing algorithm known as Survey Propagation (SP), which is empirically quite effective in solving random K − SAT instances, even when the density is close to the satisfiability threshold. We contribute to the theoretical understanding of SP by deriving the SP equations from the BP message update rules. I would like to thank Prof. Kurt Melhorn for giving me the opportunity to pursue this thesis under his supervision and his timely and valuable inputs. I am grateful to my advisor, Konstantinos Panagiotou for bringing an interesting and challenging research topic to my attention. I also thank him for his persistent support and patience through many discussions we had through the course of the thesis. He has been an excellent advisor. I thank my parents for being a source of continued emotional support and teaching me to aim high. I am thankful to all my friends for their support and encouragement.
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