Hashing practice: analysis of hashing and universal hashing
SIGMOD '88 Proceedings of the 1988 ACM SIGMOD international conference on Management of data
Practical minimal perfect hash functions for large databases
Communications of the ACM
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Expected Length of the Longest Probe Sequence in Hash Code Searching
Journal of the ACM (JACM)
An Exact Probability Model for Finite Hash Tables
Proceedings of the Fourth International Conference on Data Engineering
IEEE Transactions on Computers
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Hashing is a widely used technique for data organization. Hash tables enable a fast search of the stored data and are used in a variety of applications ranging from software to network equipment and computer hardware. One of the main issues associated with hashing are collisions that cause an increase in the search time. A number of alternatives have been proposed to deal with collisions. One of them is separate chaining, in which for each hash value an independent list of the elements that have that value is stored. In this scenario, the worst case search time is given by the maximum length of that list across all hash values. This worst case is often referred to as Longest Length Probe Sequence (llps) in the literature. Approximations for the expected longest length probe sequence when the hash table is large have been proposed and an exact analytical solution has also been presented in terms of a set of recurring equations. In this paper, a novel analytical formulation of the expected longest length probe sequence is introduced. The new formulation does not require a recursive computation and can be easily implemented in a symbolic computation tool.