The Cost of Troubleshooting Cost Clusters with Inside Information

Decision theoretical troubleshooting is about minimizing the expected cost of solving a certain problem like repairing a complicated man-made device. In this paper we consider situations where you have to take apart some of the device to get access to certain clusters and actions. Specifically, we investigate troubleshooting with independent actions in a tree of clusters where actions inside a cluster cannot be performed before the cluster is opened. The problem is non-trivial because there is a cost associated with opening and closing a cluster. Troubleshooting with independent actions and no clusters can be solved in O(n · lg n) time (n being the number of actions) by the well-known ”P-over-C” algorithm due to Kadane and Simon, but an efficient and optimal algorithm for a tree cluster model has not yet been found. In this paper we describe a ”bottom-up P-over-C” O(n · lg n) time algorithm and show that it is optimal when the clusters do not need to be closed to test whether the actions solved the problem.