Applications of Balanced Tree Search.

by Bennett L. Fox

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A discussion of the new balanced tree searching technique and its use in accelerating incremental allocation and branch and bound algorithms. Balanced tree searching is an efficient scheme for finding an item of a given value in a list, inserting an item of a given value in an appropriate place in a list, and removing an item of a given value from a list. A critical feature is that the method permits the item of maximal (or minimal) rank to be found easily, without the necessity of knowing its value in advance. The method requires that the list be maintained as a "balanced tree" so that search time will remain logarithmic and later searches, inserts, and removals can be made with equal ease. An upper bound on both the search time and the insert/removal time is proportional to the log of the number of items on the list--a speed that possibly cannot be materially improved. Although balanced tree searching requires more programming effort (and more storage), this additional work pays off for large problems. 20 pp. Refs

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