Decision-Theoretic Troubleshooting: Hardness of Approximation

TL;DR

This paper investigates the computational complexity of approximate troubleshooting strategies in decision-theoretic models, proving NP-hardness and establishing a connection to set-covering problems.

Contribution

It demonstrates that computing approximate troubleshooting strategies is NP-hard, extending the understanding of complexity in Bayesian network-based troubleshooting.

Findings

Computing approximate troubleshooting strategies is NP-hard.

The problem is closely related to set-covering problems.

Efficient algorithms are limited for complex variants.

Abstract

Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The problem has received considerable attention over the past two decades. Efficient solution algorithms have been found for simple cases, whereas other variants have been proven NP-complete. We study several variants of the problem found in literature, and prove that computing approximate troubleshooting strategies is NP-hard. In the proofs, we exploit a close connection to set-covering problems.