The Cost of Troubleshooting Cost Clusters with Inside Information
This work addresses an incremental improvement in decision theoretical troubleshooting for scenarios involving clustered actions, providing an efficient solution where none existed before.
The paper tackles the problem of minimizing expected troubleshooting costs in a tree cluster model where actions inside clusters cannot be performed before clusters are opened, and presents a 'bottom-up P-over-C' algorithm that runs in O(n lg n) time and is optimal under specific conditions.
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.