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Linear hashing and spiral storage are two dynamic hashing schemes originally designed for external files. This paper shows how to adapt these two methods for hash tables stored in main memory. The necessary data structures and algorithms are described, the expected performance is analyzed mathematically, and actual execution times are obtained and compared with alternative techniques. Linear hashing is found to be both faster and easier to implement than spiral storage. Two alternative techniques are considered: a simple unbalanced binary tree and double hashing with periodic rehashing into a larger table. The retrieval time of linear hashing is similar to double hashing and substantially faster than a binary tree, except for very small trees. The loading times of double hashing (with periodic reorganization), a binary tree, and linear hashing are similar. Overall, linear hashing is a simple and efficient technique for applications where the cardinality of the key set is not known in advance.

When the space allocation for a hash-coded table is altered, the table entries must be rescattered over the new space. A technique for accomplishing this rescattering is presented. The technique is independent of both the length of the table and the hashing function used, and can be utilized in conjunction with a linear reallocation of the table being rescattered. Moreover, it can be used to eliminate previously flagged deletions from any hash-coded table, or to change from one hashing method to another. The efficiency of the technique is discussed and theoretical statistics are given.

Secondary clustering as a cause of hash code inefficiency is discussed, and a new hashing method based on its eliminiation is presented. Comparisons with previous methods are made both analytically and empirically.

A new method of hash coding is presented and is shown to possess desirable attributes. Specifically, the algorithm is simple, efficient, and exhaustive, while needing little time per probe and using few probes per lookup. Performance data and implementation hints are also given.