Algorithms [Sedgewick, Robert]

17. Radix Searching

Several searching methods proceed by examining the search keys one bit at a time (rather than using full comparisons between keys at each step). These methods, called radix searching methods, work with the bits of

the keys themselves, as opposed to the transformed version of the keys used in hashing. As with radix sorting methods, these methods can be useful when the bits of the search keys are easily accessible and the values of the search keys are well distributed.

The principal advantages of radix searching methods are that they provide reasonable worst-case performance without the complication of balanced trees; they provide an easy way to handle variable-length keys; some allow some savings in space by storing part of the key within the search structure; and they can provide very fast access to data, competitive with both binary search trees and hashing. The disadvantages are that biased data can lead to degenerate trees with bad performance (and data comprised of characters is biased) and that some of the methods can make very inefficient use of space. Also, as with radix sorting, these methods are designed to take advantage of particular characteristics of the computer’s architecture: since they use digital properties of the keys, it’s difficult or impossible to do efficient implementations in languages such as Pascal.

We’ll examine a series of methods, each one correcting a problem inherent in the previous one, culminating in an important method which is quite useful for searching applications where very long keys are involved. In addition, we’ll see the analogue to the “linear-time sort” of Chapter 10, a “constant-time” search which is based on the same principle.

Digital Search Trees

The simplest radix search method is digital tree searching: the algorithm is precisely the same as that for binary tree searching, except that rather than

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