# 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

- Mathematics, Computer ScienceTALG
- 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

- Mathematics, Computer ScienceCombinatorics, 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

- 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

- Computer Science, 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

- Computer Science, 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

- Computer Science, 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

- Mathematics, 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, Mathematics
- 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

- Mathematics
- 2004

Two-way chaining is a novel hashing scheme that uses two independent truly uniform hash functions f and g to insert m keys into a hash table with n chains, where each key x is inserted into the…

## References

SHOWING 1-10 OF 46 REFERENCES

Individual displacements for linear probing hashing with different insertion policies

- Mathematics, Computer ScienceTALG
- 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 → ∞.

Analysis of hashing algorithms and a new mathematical transform

- Mathematics
- 1996

The main contribution of this thesis is the introduction of a new mathematical tool that we call the Diagonal Poisson Transform, and its application to the analysis of some linear probing hashing…

On the Analysis of Linear Probing Hashing

- Mathematics, Computer ScienceAlgorithmica
- 1998

Abstract. This paper presents moment analyses and characterizations of limit distributions for the construction cost of hash tables under the linear probing strategy. Two models are considered, that…

Robin hood hashing

- Computer Science26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
- 1985

This paper deals with hash tables in which conflicts are resolved by open addressing with a very simple insertion procedure which leads to a new search procedure which requires only a constant number of probes, on average, even for full tables.

The diagonal Poisson transform and its application to the analysis of a hashing scheme

- Mathematics
- 1997

We present an analysis of the effect of the last-come-first-served heuristic on a linear probing hash table. We study the behavior of successful searches, assuming searches for all elements of the…

Analysis of Uniform Hashing

- Computer ScienceJACM
- 1983

Earlier analyses of umform hashing are extended here to multlrecord buckets and three different situations are analysed: initial loadmg assuming uniform access frequencies, frequency loading assuming nonuniformAccess frequencies, and the dynamic behavior when msertions and deletions occur.

Extendible hashing—a fast access method for dynamic files

- Computer ScienceACM Trans. Database Syst.
- 1979

This work studies, by analysis and simulation, the performance of extendible hashing and indicates that it provides an attractive alternative to other access methods, such as balanced trees.

Efficient Ordering of Hash Tables

- Mathematics, Computer ScienceSIAM J. Comput.
- 1979

A scheme for reordering the table as new elements are added is presented and the minimax problem of ordering the table so as to minimize the length of the longest probe sequence to find any element is presented.

The Analysis of Linear Probing Sort by the Use of a New Mathematical Transform

- Mathematics, Computer ScienceJ. Algorithms
- 1984