The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Cost-based abduction and MAP explanation
Artificial Intelligence
Simple characterizations of P(#P) and complete problems
Journal of Computer and System Sciences
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
Approximating MAPs for belief networks is NP-hard and other theorems
Artificial Intelligence
On the complexity of unique solutions
Journal of the ACM (JACM)
A dynamic Bayesian network for diagnosing ventilator-associated pneumonia in ICU patients
Expert Systems with Applications: An International Journal
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Complexity results and approximation strategies for MAP explanations
Journal of Artificial Intelligence Research
Most probable explanations in Bayesian networks: Complexity and tractability
International Journal of Approximate Reasoning
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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.