The maximum weight hierarchy matching problem

We study the problem of fusing several reports about a group of objects into a single summary report, which best represents the received reports. A report is a list of labels associated with a group of objects, as reported by some identification device. Reports do not associate which object in the group has been given a specific label, the labels used in each report may be given in various levels of specificity and the information in the reports may be erroneous. Each label used in a report is accompanied by a weight, which provides a confidence measure for the label. The maximum weight hierarchy matching problem seeks a consistent interpretation of the received reports by matching the labels of each object across the reports, such that the total weight of elements used in the matching is maximized. In this paper we prove that this problem is NP-hard and develop an 0.632OPT approximation algorithm, where OPT is the optimal solution. The algorithm shows robust performance in Monte-Carlo simulations.