Some Combinatorial Properties of Certain Trees With Applications to Searching and Sorting
Journal of the ACM (JACM)
Variable length tree structures having minimum average search time
Communications of the ACM
Use of tree structures for processing files
Communications of the ACM
Automatic Information Organization and Retrieval.
Automatic Information Organization and Retrieval.
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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.