CCTree: An Efficient Algorithm for Mining Closed and Maximal Contiguous SubtreesTrees are a fundamental structure for representing hierarchical data such as family trees, organizational charts, and mo......

CCTree: An Efficient Algorithm for Mining Closed and Maximal Contiguous Subtrees

Trees are a fundamental structure for representing hierarchical data such as family trees, organizational charts, and molecular structures. In many applications, it is essential to identify all the contiguous subtrees that satisfy certain constraints, such as maximal or closedness. Closedness means that all the children of a node are also contained in the subtree, while maximality ensures that no proper superset satisfies the same condition. In this article, we introduce CCTree, an efficient algorithm for mining closed and maximal contiguous subtrees from a given tree.

CCTree operates in a bottom-up manner by recursively computing the closed and maximal contiguous subtrees of each node. The algorithm maintains two sets of partial results: one for the closed subtrees and another for the maximal ones. The closed set is initialized with the singleton subtrees consisting of each node, while the maximal set is empty. Then, for each inner node, CCTree combines the partial results of its children to form its own closed and maximal subtrees. The closed ones are obtained by intersecting the children's closed sets and adding the node itself, while the maximal ones are obtained by taking the union of the children's maximal sets and adding the node if it satisfies the maximal condition.

To efficiently compute the closed and maximal sets, CCTree uses two key data structures: the transaction tree and the prefix tree. The transaction tree represents the containment relations among the subtrees, where a transaction is a set of contiguous subtrees that are contained in a common parent subtree. The prefix tree represents the frequency of each subtree as a prefix path, where a prefix path is a path from the root to a leaf that corresponds to a contiguous subtree.

CCTree first constructs the transaction tree by scanning the tree from the leaves to the root and grouping the subtrees by their common parent. Then, for each transaction, CCTree computes its frequent prefixes by traversing the prefix tree along the path of each subtree and incrementing the corresponding frequency count. Finally, the frequent prefixes are used to generate the closed and maximal sets of each node.

Experimental results on various real and synthetic datasets show that CCTree outperforms state-of-the-art algorithms for mining closed and maximal contiguous subtrees in terms of both time and space efficiency. Moreover, CCTree scales well with the size and degree of the input tree, making it suitable for large-scale applications such as bioinformatics and web mining.

In conclusion, CCTree is a practical and effective algorithm for mining closed and maximal contiguous subtrees in a tree structure. Its main advantages are its bottom-up approach, its use of transaction and prefix trees, and its scalability to large datasets. We believe that CCTree has the potential to contribute to many areas of research and industry that rely on tree data mining.