On comparing bills of materials: a similarity/distance measure for unordered trees

Many enterprise areas, such as marketing, variant design, group technology, and cellular manufacturing, require their wide variety of products to be organized into families, which are clusters of similar products. In this paper, we propose a similarity metric for finding the distance between existing products based on bills of materials (BOMs), a class of unordered trees. We show that existing editing operations for unordered trees are not consistent for BOMs, and present a similarity metric based on the symmetric difference. We also provide an polynomial time algorithm for finding the minimum weighted symmetric difference between a pair of unordered trees. The results of the pairwise comparisons are used as a distance metric for a clustering algorithm that groups the BOM trees into product families.