A Constant Update Time Finger Search Tree

Paul F. Dietz, Rajeev Raman

Abstract: Levcopolous and Overmars (Acta Inform., 26 (1988) 269-277) describe a search tree with O(1) worst-case update time, i.e., the time to insert or delete a key is O(1) in the worst case if the position of the key is known. Their data structure does not support fingers, pointers to specific keys such that access and update operations in the vicinity of a finger are especially efficient. We modify their data structure to support fingers while still maintaining O(1) worst-case update time, partially improving upon an earlier result of Harel (University of California, Davis, TR #154, 1980) who achieved O(log* n) worst-case update time in a search tree with fingers. Our data structure uses the random-access machine (RAM) model with unit-cost measure and logarithmic word size; the data structures of Levcopolous and Overmars and Harel use the weaker pointer machine model.