Algorithms and software for calculating and visualizing the cardinality of the grand bounding ball by means of intersection trees

While it is straightforward to calculate the bounding ball of a partially resolved phylogenetic tree, the calculation of the cardinality of the grand bounding ball for multiple partially resolved trees is very time-consuming due to the power set principle that governs the highly iterative calculation process. What can further complicate the calculation is that the practitioner has to possess domain knowledge in phylogenetic trees, subtree mining and discrete math at the same time. This paper presents the first efficient software to automate the process of calculating the cardinality of the grand bounding ball by combining a number of advanced data mining techniques and concepts including systematically growing intersection trees, which is specially defined for this work, level by level, cluster sets, Apriori, equivalence class, and set theory, and rooting unrooted trees etc. The algorithms are discussed in the the rooted tree scope first; then they are extended to the unrooted tree scope by using a novel directing method. In addition, a displayer component has been implemented to help visualize the complicated calculation process demanded by the problem. The software is expected to be useful in phylogenetic tree clustering research.