this paper trade-offs among certain computational factors in hash coding are analyzed. The paradigm problem considered is that of testing a series of messages one-by-one for membership in a given set of messages. Two new hash- coding methods are examined and compared with a particular conventional hash-coding method. The computational factors considered are the size of the hash area (space), the time required to identify a message as a nonmember of the given set (reject time), and an allowable error frequency

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period of search for the quadratic and related hash methods

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Abstract: After a brief introduction to hash-coding (scatter storage) and discussion of methods described in the literature, it is shown that for hash tables of length p>2, prime, the primitive roots r of the cyclic group Z/p of prime residues mod p can be used for a simple collision strategy q(p,i) = r i mod p for f i(k) = f 0(k) +q(p,i) mod p. It is similar to the strategy which uses quadratic residues q(p,i) = i 2 mod p in avoiding secondary clustering, but reaches all table positions for probing. A table of n primes for typical table lengths and their primitive roots is added. In cases where r = 2 j is such a primitive root, the collision strategy can be implemented simply by repeated shifts to the left (by j places in all). To make the paper self-contained and easy to read, the relevant definitions and the theorems used from the Theory of Numbers are included in the paper.

A document retrieval system must have some means of recording the subject matter of each document in its data base. Some systems store the

Scatter storage schemes are examined with respect to their applicability to dictionary lookup procedures. Of particular interest are virtual scatter methods which combine the advantages of rapid search speed and reason- • able storage requirements. The theoretical aspects of computing hash addresses are developed, and several algorithms are evaluated. Finally, experiments with an actual text lookup process are described, and a possible library application is discussed. A document retrieval system must have some means of recording the subject matter of each document in its data base. Some systems store the actual text words, while others store keywords or similar content indicators. The SMART system ( 1) uses concept numbers for this purpose, each number indicating that a certain word appears in the document. Two advantages are apparent. First, a concept number can be held in a fixed-sized storage element. This produces faster processing than if variable-sized keywords were used. Second, the amount of storage required to hold