# Exact distribution of individual displacements in linear probing hashing

@article{Viola2005ExactDO, title={Exact distribution of individual displacements in linear probing hashing}, author={Alfredo Viola}, journal={ACM Trans. Algorithms}, year={2005}, volume={1}, pages={214-242} }

This paper studies the distribution of individual displacements for the standard and the Robin Hood linear probing hashing algorithms. When the a table of size m has n elements, the distribution of the search cost of a random element is studied for both algorithms. Specifically, exact distributions for fixed m and n are found as well as when the table is α-full, and α strictly smaller than 1. Moreover, for full tables, limit laws for both algorithms are derived.

## 23 Citations

Individual displacements for linear probing hashing with different insertion policies

- MathematicsTALG
- 2005

It is shown, using the diagonal Poisson transform studied by Poblete, Viola and Munro, that exact expressions for finite m and n can be obtained from the limits as m,n → ∞.

The Maximum Displacement for Linear Probing Hashing

- MathematicsCombinatorics, Probability and Computing
- 2013

The maximum displacement for linear probing hashing is studied using the standard probabilistic model together with the insertion policy known as First-Come-(First-Served), which focuses on dense hash tables.

Distributional analysis of Robin Hood linear probing hashing with buckets

- Mathematics
- 2006

This paper presents the first distributional analysis of a linear probing hashing scheme with buckets of size b . The exact distribution of the cost of successful searches for a bα -full table is…

Distributional analysis of Robin Hood linear probing hashing with buckets

- Mathematics
- 2005

This paper presents the first distributional analysis of a linear probing hashing scheme with buckets of size b. The exact distribution of the cost of successful searches for a bα-full table is…

Distributional Analysis of the Parking Problem and Robin Hood Linear Probing Hashing with Buckets

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2010

This paper presents the first distributional analysis of both, a parking problem and a linear probing hashing scheme with buckets of size b, and uses a new family of numbers, called Tuba Numbers, that satisfies a recurrence resembling that of the Bernoulli numbers.

A Unified Approach to Linear Probing Hashing with Buckets

- MathematicsAlgorithmica
- 2015

A unified analysis of linear probing hashing with a general bucket size is given, using the symbolic method (based on q-calculus) to directly derive the generating functions to analyze.

Individual Displacements in Hashing with Coalesced Chains

- MathematicsCombinatorics, Probability and Computing
- 2008

This work studies the asymptotic distribution of the displacements in hashing with coalesced chains, for both late-insertion and early- Insertion, using Poissonization and some stochastic calculus.

A New Approach to Analyzing Robin Hood Hashing

- Computer ScienceANALCO
- 2016

It is shown that a simple but apparently unstudied approach for handling deletions with Robin Hood hashing offers good performance even under high loads.

Random hypergraphs for hashing-based data structures

- Computer Science
- 2020

This thesis examines how hyperedge distribution and load affects the probabilities with which these properties hold and derive corresponding thresholds, and identifies a hashing scheme that leads to a particularly high threshold value in this regard.

Two-way hashing with separate chaining and linear probing

- Computer Science, Mathematics
- 2004

An Ω(log log n) universal lower bound is proved on the worst-case search time of any two-way linear probing algorithm, where n is the hash table size.

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