In computer science, an (a,b) tree is a kind of balanced search tree. An (a,b)-tree has all of its leaves at the same depth, and all internal nodes except for the root have between and children, where and are integers such that . The root has, if it is not a leaf, between 2 and children. Definition Let , be positive integers such that . Then a rooted tree is an (a,b)-tree when: Every inner node except the root has at least and at most children. The root has at most children. All paths from the root to the leaves are of the same length. Internal node representation Every internal node of a (a,b)-tree has the following representation: Let be the number of child nodes of node . Let be pointers to child nodes. Let be an array of keys such that equals the largest key in the subtree pointed to by . See also B-tree 2-3 tree 2-4 tree References Search trees