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Minimum Search Tree Structures for Data Partitioned into Pages

The doubly chained tree structure is an efficient device for organizing a file that must be searched and updated frequently. This paper considers a variation to the doubly chained tree which is more representative of a file in which the data is partitioned into blocks or pages. In this model the cost of searching the next node is 1 if the node is reachable from the same root (i.e., on the same page), and is k if the next node is the next root (i. e., on a different page). An algorithm for constructing doubly chained trees having any number of terminal nodes N, with minimal average search length, is developed. A simple closed expression is derived for the minimum average search time as a function of the number of terminal nodes N and the parameter k. A proof of optimality is also included.