The Complexity of Finding kth Most Probable Explanations in Probabilistic Networks

In modern decision-support systems, probabilistic networks model uncertainty by a directed acyclic graph quantified by probabilities. Two closely related problems on these networks are the KTH MPE and KTH PARTIAL MAP problems, which both take a network and a positive integer k for their input. In the KTH MPE problem, given a partition of the network's nodes into evidence and explanation nodes and given specific values for the evidence nodes, we ask for the kth most probable combination of values for the explanation nodes. In the KTH PARTIAL MAP problem in addition a number of unobservable intermediate nodes are distinguished; we again ask for the kth most probable explanation. In this paper, we establish the complexity of these problems and show that they are FPPP - and FPPPPP-complete, respectively.

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