O(1) Insertion for Random Walk d-ary Cuckoo Hashing up to the Load Threshold

Fuente: arXiv
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Main Authors: Bell, Tolson, Frieze, Alan
Format: Preprint
Published: 2024
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author Bell, Tolson
Frieze, Alan
author_facet Bell, Tolson
Frieze, Alan
contents The random walk $d$-ary cuckoo hashing algorithm was defined by Fotakis, Pagh, Sanders, and Spirakis to generalize and improve upon the standard cuckoo hashing algorithm of Pagh and Rodler. Random walk $d$-ary cuckoo hashing has low space overhead, guaranteed fast access, and fast in practice insertion time. In this paper, we give a theoretical insertion time bound for this algorithm. More precisely, for every $d\ge 3$ random hashes, let $c_d^*$ be the sharp threshold for the load factor at which a valid assignment of $cm$ objects to a hash table of size $m$ exists with high probability. We show that for any $d\ge 3$ hashes and load factor $c<c_d^*$, the expectation of the random walk insertion time is $O(1)$, that is, a constant depending only on $d$ and $c$ but not $m$.
format Preprint
id arxiv_https___arxiv_org_abs_2401_14394
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle O(1) Insertion for Random Walk d-ary Cuckoo Hashing up to the Load Threshold
Bell, Tolson
Frieze, Alan
Data Structures and Algorithms
Combinatorics
68Q25
F.2.2; E.2
The random walk $d$-ary cuckoo hashing algorithm was defined by Fotakis, Pagh, Sanders, and Spirakis to generalize and improve upon the standard cuckoo hashing algorithm of Pagh and Rodler. Random walk $d$-ary cuckoo hashing has low space overhead, guaranteed fast access, and fast in practice insertion time. In this paper, we give a theoretical insertion time bound for this algorithm. More precisely, for every $d\ge 3$ random hashes, let $c_d^*$ be the sharp threshold for the load factor at which a valid assignment of $cm$ objects to a hash table of size $m$ exists with high probability. We show that for any $d\ge 3$ hashes and load factor $c<c_d^*$, the expectation of the random walk insertion time is $O(1)$, that is, a constant depending only on $d$ and $c$ but not $m$.
title O(1) Insertion for Random Walk d-ary Cuckoo Hashing up to the Load Threshold
topic Data Structures and Algorithms
Combinatorics
68Q25
F.2.2; E.2
url https://arxiv.org/abs/2401.14394