The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A Note on the Efficiency of Hashing Functions
Journal of the ACM (JACM)
Reducing the retrieval time of scatter storage techniques
Communications of the ACM
Communications of the ACM
The analysis of hashing algorithms.
The analysis of hashing algorithms.
The Analysis of Hashing Techniques That Exhibit k-ary Clustering
Journal of the ACM (JACM)
A Survey of Analysis Techniques for Discrete Algorithms
ACM Computing Surveys (CSUR)
The analysis of an improved hashing technique
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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In this paper we analyze the performance of a well known algorithm known as double hashing [Knuth]. In this method we probe the hash table along arithmetic progressions, where both the initial element and the increment of the progression are chosen randomly and independently depending only on the key K of the search. We prove that double hashing is asymptotically equivalent to uniform probing, an idealized hashing technique that exhibits no clustering and is known to be optimal in a certain sense. Between steps of the extension process we can show that the effect of clustering is negligible, and that we therefore never depart too far from the truly random situation.