Distributional analysis of Robin Hood linear probing hashing with buckets
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 $b \alpha$ -full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/3386/pdf |
| _version_ | 1797270630927695872 |
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| author | Alfredo Viola |
| author_facet | Alfredo Viola |
| author_sort | Alfredo Viola |
| collection | DOAJ |
| description | 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 $b \alpha$ -full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributional results are also obtained for tables of size $m$ and $n$ elements. A key element in the analysis is the use of a new family of numbers that satisfies a recurrence resembling that of the Bernoulli numbers. These numbers may prove helpful in studying recurrences involving truncated generating functions, as well as in other problems related with buckets. |
| first_indexed | 2024-04-25T02:07:20Z |
| format | Article |
| id | doaj.art-6e1cdf1116cd4c2cbeee476fc41f76b2 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:07:20Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-6e1cdf1116cd4c2cbeee476fc41f76b22024-03-07T14:30:52ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AD,...Proceedings10.46298/dmtcs.33863386Distributional analysis of Robin Hood linear probing hashing with bucketsAlfredo Viola0Universidad de la República [Montevideo]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 $b \alpha$ -full table is obtained, and moments and asymptotic results are derived. With the use of the Poisson transform distributional results are also obtained for tables of size $m$ and $n$ elements. A key element in the analysis is the use of a new family of numbers that satisfies a recurrence resembling that of the Bernoulli numbers. These numbers may prove helpful in studying recurrences involving truncated generating functions, as well as in other problems related with buckets.https://dmtcs.episciences.org/3386/pdfdistributional analysishashinglinear probingbuckets[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co][info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| spellingShingle | Alfredo Viola Distributional analysis of Robin Hood linear probing hashing with buckets Discrete Mathematics & Theoretical Computer Science distributional analysis hashing linear probing buckets [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| title | Distributional analysis of Robin Hood linear probing hashing with buckets |
| title_full | Distributional analysis of Robin Hood linear probing hashing with buckets |
| title_fullStr | Distributional analysis of Robin Hood linear probing hashing with buckets |
| title_full_unstemmed | Distributional analysis of Robin Hood linear probing hashing with buckets |
| title_short | Distributional analysis of Robin Hood linear probing hashing with buckets |
| title_sort | distributional analysis of robin hood linear probing hashing with buckets |
| topic | distributional analysis hashing linear probing buckets [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-cg] computer science [cs]/computational geometry [cs.cg] |
| url | https://dmtcs.episciences.org/3386/pdf |
| work_keys_str_mv | AT alfredoviola distributionalanalysisofrobinhoodlinearprobinghashingwithbuckets |