The new class of Pk trees is presented, where height balance is maintained for the nodes lying on particular paths. The number of nodes of a Pk tree asympotically grows as a power of the height, in the worst case. A procedure for node insertion is given, and the class of trees considered is restricted to IPk trees, which are buildable by such a procedure. The average behavior of such trees, studied by an extensive set of simulation runs, is close to that of AVL trees. In particular, the family of IP0 trees whose main advantage is the reduced number of restructurings required after node insertion, is analyzed.
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