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In this paper we are adding partial persistence to a balanced search tree with a worst case constant update time  (in the case that the position of the update is given), via the node-copying method .
The idea in  is to organize the leaves of an (a, b) tree into buckets, with each bucket containing O(h) leaves, where h is the height of tree. A brief description of the structure is as follows: In every bucket, a pointer (called r_pointer) is stored, that points to an ancestor (or to a node “near” an ancestor) of the bucket. When an update occurs inside the bucket, we follow the r_pointer, rebalance the pointed ancestor and set the r_pointer to point one level upwards. After each such step, the bucket is split incrementally and, when the r_pointer reaches the root of the tree, the incremental process completes. Let u be the node pointed by the r_pointer of a bucket. To rebalance u, the following actions are performed: If u has more than b children (we call such a node big), u is split into two small nodes otherwise u is left intact (we call such a node small). In either case, the r_pointer is moved up one level. It is proved in  that, starting from an (α, b)-tree, this algorithm produces an (α, 2b)-tree.